Singularities of invariant connections

Abstract

A reductive homogeneous space M = P/G is considered, endowed with an invariant connection, i.e., such that all left translations of M induced by members of P preserve it. We study the set of singularities of such connections giving sufficient conditions for it to be empty, or, in other cases, families of b-incomplete curves converging to singularities. A full description of the b-completion of a connection with M = R(m) (or a quotient of it) is given with information on its topology.