Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles

TL;DR

This paper explores the geometric structures on cotangent bundles of Riemannian manifolds, specifically focusing on natural diagonal almost product, para-Hermitian, and para-Kählerian structures, providing new characterizations.

Contribution

It introduces and characterizes natural diagonal almost product and para-Hermitian structures on cotangent bundles, expanding the understanding of their geometric properties.

Findings

Characterization of natural diagonal (almost) para-Kählerian structures

Construction of natural diagonal almost product and para-Hermitian structures

Identification of conditions for these structures to be integrable or special

Abstract

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem for the natural diagonal (almost) para-K\"ahlerian structures on the total spaces of the cotangent bundle.