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Spinor equations in Weyl geometry. (English) Zbl 0983.53028

Slovák, Jan (ed.) et al., The proceedings of the 19th Winter School “Geometry and physics”, Srní, Czech Republic, January 9-15, 1999. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 63, 63-73 (2000).
This paper deals with Dirac, twistor and Killing equations on Weyl manifolds with \(C\)-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.
For the entire collection see [Zbl 0940.00040].

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C27 Spin and Spin\({}^c\) geometry
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