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Annals of Global Analysis and Geometry

, Volume 55, Issue 2, pp 181–196 | Cite as

Parallel spinors and basic holonomy in pseudo-Hermitian geometry

  • Felipe LeitnerEmail author
Article

Abstract

We introduce in this paper an adjustment for the Webster–Tanaka connection of pseudo-Hermitian geometry on CR manifolds, which behaves naturally with respect to issues concerning parallel sections and holonomy. We call this connection and its holonomy group basic. The basic holonomy group is suitable to describe pseudo-Einstein spaces. Moreover, for pseudo-Hermitian spin manifolds, we discuss the existence of (transversally) parallel spinors. Such spinors exist on pseudo-Einstein spaces, no matter of the sign of the Webster scalar curvature.

Keywords

CR geometry Pseudo-Einstein structures Holonomy Parallel spinors 

Mathematics Subject Classification

Primary 32V05 53C27 53C29 Secondary 53C17 53C25 53C55 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Institut für Mathematik und InformatikUniversität GreifswaldGreifswaldGermany

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