Spinor equations in Weyl geometry
Differential Geometry
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.math/9901125,
title = {Spinor equations in Weyl geometry},
author = {Volker Buchholz},
journal= {arXiv preprint arXiv:math/9901125},
year = {2007}
}
Comments
Latex2.09, 11 pages