Lie Groups as 4-Dimensional Riemannian or Pseudo-Riemannian Almost Product Manifolds with Nonintegrable Structure

Abstract

A Lie group as a 4-dimensional pseudo-Riemannian manifold is considered. This manifold is equipped with an almost product structure and a Killing metric in two ways. In the first case Riemannian almost product manifold with nonintegrable structure is obtained, and in the second case – a pseudo-Riemannian one. Each belongs to a 4-parametric family of manifolds, which are characterized geometrically.