Torsion free equiaffine connections on three-dimensional homogeneous spaces

Abstract

The aim of this paper is to describe equiaffine connections on three-dimensional homogeneous spaces. The affine connection is equiaffine if it admits a parallel volume form. Only the case of spaces not admitting connections with nonzero torsion is considered. For such homogeneous spaces, it is determined under what conditions the connection is equiaffine (locally equiaffine). In addition, equiaffine (locally equiaffine) connections and Ricci tensors are written out in explicit form. In this work we use the algebraic approach for description of connections, methods of the theory of Lie groups, Lie algebras and homogeneous spaces.