This paper deals with Dirac, twistor and Killing equations on Weyl manifolds with -spin structures. A conformal Schrödinger-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.
@article{701649,
title = {Spinor equations in Weyl geometry},
booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {2000},
pages = {63-73},
mrnumber = {MR1758080},
zbl = {0983.53028},
url = {http://dml.mathdoc.fr/item/701649}
}
Buchholz, Volker. Spinor equations in Weyl geometry, dans Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books, (2000), pp. 63-73. http://gdmltest.u-ga.fr/item/701649/