A new connection in a Riemannian manifold

TL;DR

This paper introduces a novel connection in Riemannian manifolds, generalizing several known types and providing formulas for its curvature tensor, expanding the understanding of geometric structures.

Contribution

It presents a new connection in Riemannian manifolds that encompasses existing connections and introduces some previously unconsidered types.

Findings

The new connection reduces to symmetric, semi-symmetric, and quarter-symmetric connections in special cases.

Formulas for the curvature tensor of the new connection are derived.

Some of the connections introduced are novel and have not been previously studied.

Abstract

In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter-symmetric connections; even some of them are not introduced so far. We also find formula for curvature tensor of this new connection.