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Title: Spinor equations in Weyl geometry (English)
Author: Buchholz, Volker
Language: English
Journal: Proceedings of the 19th Winter School "Geometry and Physics"
Issue: 1999
Pages: 63-73
Category: math
Summary: This paper deals with Dirac, twistor and Killing equations on Weyl manifolds with $C$-spin structures. A conformal Schr\"odinger-Lichnerowicz formula is presented and used to derive integrability conditions for these equations. It is shown that the only non-closed Weyl manifolds of dimension greater than 3 that admit solutions of the real Killing equation are 4-dimensional and non-compact. Any Weyl manifold of dimension greater than 3, that admits a real Killing spinor has to be Einstein-Weyl. (English)
MSC: 53C25
MSC: 53C27
MSC: 58J60
idZBL: Zbl 0983.53028
idMR: MR1758080
Date available: 2009-07-13T21:43:04Z
Last updated: 2012-09-18
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