P-connection on Riemannian almost product manifolds

TL;DR

This paper introduces a new linear connection called P-connection on Riemannian almost product manifolds, preserving both the structure and metric, extending concepts from Hermitian and Norden geometries.

Contribution

It defines and studies the P-connection, an analogue of known connections in Hermitian and Norden geometries, on nonintegrable Riemannian almost product manifolds.

Findings

P-connection preserves the almost product structure and metric.

Analysis of P-connection on nonintegrable manifolds.

Extension of classical connections to new geometric setting.

Abstract

In the present work, we introduce a linear connection (preserving the almost product structure and the Riemannian metric) on Riemannian almost product manifolds. This connection, called P-connection, is an analogue of the first canonical connection of Lichnerowicz in the Hermitian geometry and the B-connection in the geometry of the almost complex manifolds with Norden metric. Particularly, we consider the P-connection on a the class of manifolds with nonintegrable almost product structure.