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Timeline for Weitzenböck Identities

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Apr 13, 2017 at 12:19 history edited CommunityBot
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Aug 4, 2014 at 3:13 answer added Misha Verbitsky timeline score: 11
Jan 6, 2013 at 3:30 history edited Michael Albanese CC BY-SA 3.0
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Sep 17, 2012 at 8:28 vote accept Michael Albanese
Sep 15, 2012 at 0:46 answer added DamienW timeline score: 8
Sep 14, 2012 at 16:39 answer added Deane Yang timeline score: 8
Sep 14, 2012 at 15:07 answer added Liviu Nicolaescu timeline score: 23
Sep 14, 2012 at 13:30 comment added Peter Dalakov The Weitzenboeck technique is mostly used to show that some (first order, self-adjoint) differential operator $D$ (acting on sections of an hermitian bundle over a compact manifold $M$) has trivial kernel. Since the $L^2$ norm of $Ds$ is $\int_M (D^2s,s)$, the goal is to write $D^2$ as some "standard Laplacian" plus a 0-order scalar term, $D^2=\Delta +A$. If $A$ is pointwise positive, by the maximum principle for $\Delta$ you get that $Ds=0$ implies $s=0$.
Sep 14, 2012 at 12:58 comment added Paul Reynolds This paper, although written from a Riemannian geometry perspective instead of a complex one, has a seemingly general definition of Weitzenb\"ock identity. It's a bit long though. arxiv.org/abs/math/0702031
Sep 14, 2012 at 12:53 answer added Peter Dalakov timeline score: 9
Sep 14, 2012 at 12:52 comment added Gunnar Þór Magnússon Demailly's book (www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf) and Besse's "Einstein manifolds" have good discussions of these things. The identity you write is called a Bochner-Kodaira-Nakano identity, which is a complex geometric version of a Weitzenböck identity. By any name, these things express the difference between two Laplacians.
Sep 14, 2012 at 12:07 history asked Michael Albanese CC BY-SA 3.0