Skew Killing spinors in four dimensions

Autor: Ines Kath, Nicolas Ginoux, Georges Habib
Přispěvatelé: Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Lebanese University [Beirut] (LU), Institut für Mathematik und Informatik, The second named author would like to thank the Alexander von Humboldt foundation and the DAAD for the financial support
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Annals of Global Analysis and Geometry
Annals of Global Analysis and Geometry, Springer Verlag, In press, ⟨10.1007/s10455-021-09754-9⟩
HAL
ISSN: 0232-704X
1572-9060
DOI: 10.1007/s10455-021-09754-9⟩
Popis: This paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor $$\psi $$ ψ is a spinor that satisfies the equation $$\nabla _X\psi =AX\cdot \psi $$ ∇ X ψ = A X · 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 $${\mathbb {R}}\times N$$ 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 $${\mathbb {S}}^2\times {\mathbb {R}}^2$$ 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.
Databáze: OpenAIRE
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