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Advances in Applied Clifford Algebras

, Volume 24, Issue 3, pp 737–768 | Cite as

Connections on Cahen-Wallach Spaces

  • Frank Klinker
Article

Abstract

We systematically discuss connections on the spinor bundle of Cahen-Wallach symmetric spaces. A large class of these connections is closely connected to a quadratic relation on Clifford algebras. This relation in turn is associated to the symmetric linear map that defines the underlying space. We present various solutions of this relation. Moreover, we show that the solutions we present here provide a complete list with respect to a particular algebraic condition on the parameters that enter into the construction.

Keywords

Spinor connection Cahen-Wallach space homogeneous structure quadratic Clifford pair 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Faculty of Mathematics, TU Dortmund UniversityDortmundGermany

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