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.Comment: Latex2.09, 11 page

Buchholz, Volker

English

arXiv

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

Czech digital mathematics library

Spinor equations in Weyl geometry

: In this paper, the Dirac, twistor and Killing equations are investigated on CSpin manifolds. These are Weyl manifolds together with a CSpin structure. A conformal Schr odingerLichnerowicz formula is presented. It is used in order to show integrability conditions for the twistor and Killing equation. Subj. Class: Differential Geometry  1991 MSC: 53C05;53C10;53A30  Keywords: Weyl geometry; Dirac equation; twistor equation 0 Introduction  In this paper, we give an introduction to conformal spin geometry, i.e., spin geometry on conformal manifolds, that are additionally equipped with a Weyl structure. In the first section, we state some basic facts about Weyl manifolds. This includes the definition of density bundles, Weyl structures, curvature terms and Einstein-Weyl structures. The latter arise as necessary conditions for the existence of non-trivial real Killing spinor fields. For a more detailed approach to Weyl geometry or Einstein Weyl geometry we refer to [3] and [8]. The second s..

Volker Buchholz

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Spinor Equations in Weyl Geometry

Institute of Mathematics AS CR, v. v. i.

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.9414

Spinor equations in Weyl geometry

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Czech digital mathematics library

CiteSeerX

Institute of Mathematics AS CR, v. v. i.