We describe the possible holonomy groups of simply connected irreducible
non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel
spinors.Comment: Latex2.09, 18 page

Baum, Helga

Kath, Ines

English

arXiv

We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel spinors. 1 Introduction  In [Wa 89] McKenzie Y. Wang described the possible holonomy groups of complete simply connected irreducible non-flat Riemannian spin manifolds M  n  which admit parallel spinors. Parallel spinors occur exactly for the holonomy representations  SU(m), n = 2m  4, Sp(m), n = 4m  8, G 2 and Spin(7). A complete, simply connected locally symmetric Riemannian spin manifold with non-trivial parallel spinors is flat. In the present paper we consider the same problem for pseudo-Riemannian spin manifolds. We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds M  r;s  of dimension  r + s and index r and study the chiral type and the causal type of these parallel spinors with respect to the indefinite scalar product on the spinor bundle. The method to atta..

Helga Baum

Ines Kath

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Parallel spinors and holonomy groups on pseudo-Riemannian spin manifolds

Baum, H

Kath, I

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Parallel spinors and holonomy groups on pseudo-Riemanian spin manifolds

Parallel spinors and holonomy groups on pseudo-Riemannian spinmanifolds

Parallel spinors and holonomy groups on pseudo-Riemannian spinmanifolds

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