Timeline for Killing spinors and symmetric tensor fields.

5 events

when toggle format	what		by	license	comment
Dec 6, 2011 at 4:13	comment	added	kangdon		Hi, this probably isn't much help. Tensors (of rank two) satisfying $\nabla_Xh(Y)-\nabla_Yh(X)=0$ are also called Codazzi tensors. There are many of them (e.g $g$ or the second fundamental form) and many people find them interesting. For example: According to arxiv.org/abs/1111.7002 Berger-Ebin (projecteuclid.org/…) proved that a constant trace Codazzi tensor on a compact manifold with non-negative sectional curvature must be parallel ($\nabla h=0$).
Nov 28, 2011 at 18:38	comment	added	Spiro Karigiannis		I don't understand. You are saying that $\sum_{i=1}^n \nabla_i h(Y) \cdot \nabla_i \sigma = 0$ for every $Y$ without $\nabla h = 0$ is equivalent to what, exactly? That there exists a solution to the Laplace-type equation? If that's not what you mean (or even if it is), we might be able to help more easily if you show exactly why these two statements (or some two statements) are equivalent.
Nov 28, 2011 at 14:28	history	edited	Klaus Kröncke	CC BY-SA 3.0	added 250 characters in body
Nov 26, 2011 at 17:53	history	edited	José Figueroa-O'Farrill	CC BY-SA 3.0	added 5 characters in body
Nov 25, 2011 at 16:06	history	asked	Klaus Kröncke	CC BY-SA 3.0