Spinor equations in Weyl geometry

Details Spinor equations in Weyl geometry Spinor equations in Weyl geometry

1999-01-27

arxiv.org/abs/math/9901125v2

Mathematics

Differential Geometry

Latex2.09, 11 pages

Scientific paper

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.

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