Connections on Cahen-Wallach spaces

Abstract

We systematically discuss connections on spinor bundles of Cahen- Wallach symmetric spaces. A large class of these connections is closely connected with a quadratic relation on a Clifford algebra. This relation in turn is associated to a 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.