Some Characterizations in Kenmotsu manifolds with a new connection

TL;DR

This paper introduces a new generalized symmetric metric connection on Kenmotsu manifolds, explores its properties, and provides specific tensor calculations and an original example to illustrate the concepts.

Contribution

It proposes a new generalized symmetric metric connection on Kenmotsu manifolds and derives related tensor properties, extending existing geometric frameworks.

Findings

Derived tensor relations involving curvature, Ricci, projective, and concircular tensors.

Established conditions under the new connection on Kenmotsu manifolds.

Presented an original example illustrating the new connection.

Abstract

The present study initially identified the generalized symmetric connections $(\alpha,\beta)$ typed, which can be regarded as more generalised forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively particularly when $(\alpha,\beta)=(1,0)$ and $(\alpha,\beta)=(0,1)$ are taken into consideration. Taking that into account, a new generalized symmetric metric connection was attained upon Kenmotsu manifolds. In compliance with the new connection, some results were provided through calculation of tensors belonging to Kenmotsu manifold involving curvature tensor, ricci tensor, projective curvature tensor and coincircular curvature tensor. Ultimately, an original example was presented.