Spinor equations in Weyl geometry

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In this paper, the Dirac, twistor and Killing equations on Weyl manifolds with CSpin structures are investigated. A conformal Schr"odinger-Lichnerowicz formula is presented and used to show integrability conditions for these equations. By introducing the Killing equation for spinors of arbitrary weight, the result of Andrei Moroianu in [9] is generalized in the following sense. 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 these dimensions admitting a real Killing spinor has to be Einstein-Weyl.
Latex2.09, 11 pages

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Differential Geometry, 53C05;53C10;53A30

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http://salesiana.dossiersoluciones.com/handle/123456789/78008

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9901125
 http://arxiv.org/abs/math/9901125

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arXiv