Connections on Cahen-Wallach spaces

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 provide a complete list with respect to a particular algebraic condition on the parameters that enter into the construction.

30 pages, v3 coincides with published version. Advances in Applied Clifford Algebras, 2014

References in corpus (6)

• On the full holonomy group of special Lorentzian manifolds
• Symmetric backgrounds of type IIB supergravity
• Supersymmetric Killing Structures
• Solvable Pseudo-Riemannian Symmetric Spaces
• Lorentzian symmetric spaces in supergravity
• The Torsion of Spinor Connections and Related Structures

Cited by in corpus (1)

• A family of non-restricted $D=11$ geometric supersymmetries