On Riemannian coverings of manifolds admitting locally splitting actions

Abstract

By studying the structure of certain covering manifolds, associated with a series of subgroups of π1(M), we “approximate” the structure of the Riemannian manifoldM, provided that it admits a locally splitting action. The above series arises because of the local splitting of the action and the study is carried out via initial data. Also, we indicate how manifolds without conjugate points can be investigated using locally splitting actions of abelian Lie groups.