Curvature relations in almost product manifolds

TL;DR

This paper explores curvature relations and conformal properties of connections in almost product manifolds, deriving new identities and discussing applications in physics such as Kaluza-Klein and gauge theories.

Contribution

It introduces new curvature relations and identities for almost product manifolds, with an analysis of their conformal behavior and physical applications.

Findings

Derived new curvature component relations.

Established identities for deformation tensor parts.

Discussed applications in Kaluza-Klein and gauge theories.

Abstract

New relations involving curvature components for the various connections appearing in the theory of almost product manifolds are given and the conformal behaviour of these connections are studied. New identities for the irreducible parts of the deformation tensor are derived. Some direct physical applications in Kaluza-Klein and gauge theory are discussed.