A note over para complex torsion-free affine connection on tangent bundle

TL;DR

This paper introduces a lifting theory in differential geometry, demonstrating that the tangent bundle of a paracomplex manifold admits a para-complex torsion-free affine connection using lifted structures.

Contribution

It presents a novel application of lifting theory to establish the existence of a specific affine connection on tangent bundles of paracomplex manifolds.

Findings

Tangent bundle TM admits a para-complex torsion-free affine connection.

Lifting theory effectively constructs geometric structures on tangent bundles.

The approach enhances understanding of geometric connections in paracomplex geometry.

Abstract

The goal of this paper is to introduce the lifting theory that has an important role in geometry. Therefore, using the lifts of differential geometric structures we show that tangent bundle TM of paracomplex manifold M admits para-complex torsion-free affine connection.