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Skew Killing spinors in four dimensions

Abstract : This paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor ψ is a spinor that satisfies the equation ∇Xψ = AX · ψ with a skew-symmetric endomorphism A. We consider the degenerate case, where the rank of A is at most two everywhere and the non-degenerate case, where the rank of A is four everywhere. We prove that in the degenerate case the manifold is locally isometric to the Riemannian product R × N with N having a skew Killing spinor and we explain under which conditions on the spinor the special case of a local isometry to S 2 × R 2 occurs. In the non-degenerate case, the existence of skew Killing spinors is related to doubly warped products whose defining data we will describe.
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https://hal.archives-ouvertes.fr/hal-02560712
Contributor : Nicolas Ginoux <>
Submitted on : Thursday, July 23, 2020 - 5:37:27 PM
Last modification on : Friday, July 31, 2020 - 10:33:14 AM

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  • HAL Id : hal-02560712, version 2
  • ARXIV : 2005.01477

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Nicolas Ginoux, Georges Habib, Ines Kath. Skew Killing spinors in four dimensions. 2020. ⟨hal-02560712v2⟩

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