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More Information: <a href="http://lussumo.com/docs">Documentation</a>, <a href="http://lussumo.com/community">Community Support</a>.</p></div> <div id="Content"><div id="NoticeCollector" class="Notices"><div class="Notice"><strong>Welcome to nForum</strong> <br />If you want to take part in these discussions either <a href="/people.php?ReturnUrl=http%3A%2F%2Fnforum.ncatlab.org%2Fdiscussion%2F11532%2Fkaehler-manifold%2F">sign in now</a> (if you have an account), <a href="https://nforum.ncatlab.org/people/?PostBackAction=ApplyForm">apply for one now</a> (if you don't).</div></div><div class="ContentInfo Top"> <h1><a href="https://nforum.ncatlab.org/5/"><a href="https://nforum.ncatlab.org/18/">nLab</a> > </a> <a href="https://nforum.ncatlab.org/5/">Latest Changes</a>: Kähler manifold</h1> <a href="#pgbottom">Bottom of Page</a> <div class="PageInfo"> <p>1 to 10 of 10</p> <ol class="PageList PageListEmpty"> <li> </li> </ol> </div> </div> <div id="ContentBody"> <script type="text/javascript"> //<![CDATA[ function toggle_source(id) { var mysrc = document.getElementById("CommentBody_" + id).firstChild; if (mysrc.className == "source") { if (mysrc.style.display == "none") { mysrc.style.display = "block"; } else { mysrc.style.display = "none"; } } } var commentIds = new Array(0); function hide_sources() { for (i = 0; i < commentIds.length; i++) { var myself = document.getElementById("Source" + commentIds[i]); var mycmt = document.getElementById("CommentBody_" + commentIds[i]); if (mycmt.firstChild.className != "source") { myself.style.display = "none"; } } } window.onload = hide_sources; //]]> </script> <ol id="Comments"><li id="Comment_85809"> <a id="Item_1"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>1.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Jul 14th 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=85809#Comment_85809">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_85809"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>added publication data to * [[Andrei Moroianu]], _Lectures on K&#228;hler Geometry_, Cambridge University Press 2007 ([arXiv:math/0402223](https://arxiv.org/abs/math/0402223) [doi:10.1017/CBO9780511618666](https://doi.org/10.1017/CBO9780511618666), [pdf](https://moroianu.perso.math.cnrs.fr/tex/kg.pdf)) and pointer to section 11.1 there for Kaehler structures as torsion-free $U(n)$-structures <a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/35">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/35">v35</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></code></div><div> <p>added publication data to</p> <ul> <li><a href="https://ncatlab.org/nlab/show/Andrei Moroianu">Andrei Moroianu</a>, <em>Lectures on Kähler Geometry</em>, Cambridge University Press 2007 (<a href="https://arxiv.org/abs/math/0402223">arXiv:math/0402223</a> <a href="https://doi.org/10.1017/CBO9780511618666">doi:10.1017/CBO9780511618666</a>, <a href="https://moroianu.perso.math.cnrs.fr/tex/kg.pdf">pdf</a>)</li> </ul> <p>and pointer to section 11.1 there for Kaehler structures as torsion-free <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">U(n)</annotation></semantics></math>-structures</p> <p><a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/35">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/35">v35</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></p> </div> </div> </li><li id="Comment_85838" class="Alternate"> <a id="Item_2"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>2.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Jul 15th 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=85838#Comment_85838">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_85838"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>added pointer to * Akira Fujiki, _On primitively symplectic compact Kähler V-manifolds_, in: [[Kenji Ueno]], _Classification of Algebraic and Analytic Manifolds: Katata Symposium Proceedings 1982_, Birkhäuser 1983 (ISBN:9780817631376) <a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/38">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/38">v38</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></code></div><div> <p>added pointer to</p> <ul> <li>Akira Fujiki, <em>On primitively symplectic compact Kähler V-manifolds</em>, in: <a href="https://ncatlab.org/nlab/show/Kenji Ueno">Kenji Ueno</a>, <em>Classification of Algebraic and Analytic Manifolds: Katata Symposium Proceedings 1982</em>, Birkhäuser 1983 (ISBN:9780817631376)</li> </ul> <p><a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/38">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/38">v38</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></p> </div> </div> </li><li id="Comment_86942"> <a id="Item_3"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>3.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></li> <li><span>CommentTime</span>Sep 26th 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=86942#Comment_86942">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_86942"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Typo in the symmetry of the metric Anonymous <a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/39">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/39">v39</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></code></div><div> <p>Typo in the symmetry of the metric</p> <p>Anonymous</p> <p><a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/39">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/39">v39</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></p> </div> </div> </li><li id="Comment_105460" class="Alternate"> <a id="Item_4"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>4.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></li> <li><span>CommentTime</span>Dec 12th 2022</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=105460#Comment_105460">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_105460"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Corrected sign error when deriving the symmetry of g. Anonymous <a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/41">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/41">v41</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></code></div><div> <p>Corrected sign error when deriving the symmetry of g.</p> <p>Anonymous</p> <p><a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/41">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/41">v41</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></p> </div> </div> </li><li id="Comment_111557"> <a id="Item_5"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>5.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></li> <li><span>CommentTime</span>Jul 24th 2023</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=111557#Comment_111557">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_111557"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>just a typo in the relation between \omega and g. Alex Gomez <a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/42">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/42">v42</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></code></div><div> <p>just a typo in the relation between \omega and g.</p> <p>Alex Gomez</p> <p><a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/42">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/42">v42</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></p> </div> </div> </li><li id="Comment_119865" class="Alternate"> <a id="Item_6"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>6.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></li> <li><span>CommentTime</span>2 days ago</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=119865#Comment_119865">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_119865"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Added a section on Kapranov's structure and added literature on its reincarnations in the context of Fedosov quantization of Kahler manifolds Nikita Golub <a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/45">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/45">v45</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></code></div><div> <p>Added a section on Kapranov’s structure and added literature on its reincarnations in the context of Fedosov quantization of Kahler manifolds</p> <p>Nikita Golub</p> <p><a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/45">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/45">v45</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></p> </div> </div> </li><li id="Comment_119866"> <a id="Item_7"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>7.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>1 day ago</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=119866#Comment_119866">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_119866"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Nick, at the very end of the last theorem ([here](https://ncatlab.org/nlab/show/Kähler+manifold#KapranovTheorem)) you write "weak Lie algebra" -- I suppose that's meant to be "$L_\infty$-algebra"? <a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/46">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/46">v46</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></code></div><div> <p>Nick, at the very end of the last theorem (<a href="https://ncatlab.org/nlab/show/Kähler+manifold#KapranovTheorem">here</a>) you write “weak Lie algebra” – I suppose that’s meant to be “<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi> <mn>∞</mn></msub></mrow><annotation encoding="application/x-tex">L_\infty</annotation></semantics></math>-algebra”?</p> <p><a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/46">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/46">v46</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></p> </div> </div> </li><li id="Comment_119867" class="Alternate"> <a id="Item_8"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>8.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/3584/">NickGolub</a></li> <li><span>CommentTime</span>1 day ago</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=119867#Comment_119867">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_119867"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/3584/">NickGolub</a></span><br/><span class="sourceType">Format: Text</span><code>Ah, yes. Wanted to make the claim closer to the original.</code></div><div> Ah, yes. Wanted to make the claim closer to the original. </div> </div> </li><li id="Comment_119868"> <a id="Item_9"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>9.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>1 day ago</li><li><em>(edited 1 day ago)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=119868#Comment_119868">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_119868"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>how about writing an [[L-infinity-algebra|$L_\infty$-algebra]] (called a "weak Lie algebra" in [Kapranov 1999](#Kapranov99)) > an [[L-infinity-algebra|$L_\infty$-algebra]] (called a "weak Lie algebra" in [Kapranov 1999](#Kapranov99)) ? <a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/48">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/48">v48</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></code></div><div> <p>how about writing</p> <pre><code> an [[L-infinity-algebra|$L_\infty$-algebra]] (called a "weak Lie algebra" in [Kapranov 1999](#Kapranov99)) </code></pre> <blockquote> <p>an <a href="https://ncatlab.org/nlab/show/L-infinity-algebra"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi> <mn>∞</mn></msub></mrow><annotation encoding="application/x-tex">L_\infty</annotation></semantics></math>-algebra</a> (called a “weak Lie algebra” in <a href="#Kapranov99">Kapranov 1999</a>)</p> </blockquote> <p>?</p> <p><a href="https://ncatlab.org/nlab/revision/diff/K%C3%A4hler+manifold/48">diff</a>, <a href="https://ncatlab.org/nlab/revision/K%C3%A4hler+manifold/48">v48</a>, <a href="https://ncatlab.org/nlab/show/K%C3%A4hler+manifold">current</a></p> </div> </div> </li><li id="Comment_119869" class="Alternate"> <a id="Item_10"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>10.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/3584/">NickGolub</a></li> <li><span>CommentTime</span>1 day ago</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/11532/kaehler-manifold/?Focus=119869#Comment_119869">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_119869"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/3584/">NickGolub</a></span><br/><span class="sourceType">Format: Text</span><code>sure, this sounds better</code></div><div> sure, this sounds better </div> </div> </li></ol> </div><div class="ContentInfo Middle"> <div class="PageInfo"> <p>1 to 10 of 10</p> <ol class="PageList PageListEmpty"> <li> </li> </ol> </div> </div></div> <a id="pgbottom" > </a> </div> </div></body> </html>