Talk:Weitzenböck identity

Torsion

It might be an interesting exercise to see what these formulae look like if the connection is allowed to have torsion. This is of especial importance in the complex case for a non-Kähler metric on a complex manifold. Silly rabbit 20:16, 7 June 2006 (UTC)

Attribution to R. Weitzenböck

I removed the sloppy sentence from the introduction

(The origins of this terminology seem doubtful, however, as there does not seem to be any evidence that such identities ever appeared in Weitzenböck's work.)

— 74.101.234.187, Revision as of 20:02, 6 July 2013

that is neither referenced nor meaningful in this context. On the one hand, it is often unclear why certain notions or theorems are attributed to certain researchers, whereas, on the other hand, e.g. a reference I could find is in Petersen's book

Prior to Bochner’s work Weitzenböck developed a formula very similar to the Bochner formula. We shall also explain this related formula and how it can be used to establish the Bochner formulas we use. It appears that Weitzenböck never realized that his work could have an impact on geometry and only thought of his work as an application of algebraic invariant theory.

— Peter Petersen, Riemannian geometry (Third edition. Graduate Texts in Mathematics, 171. Springer, Cham, 2016.), p. 334

Wueb (talk) 17:49, 2 August 2021 (UTC)