On a Semi-symmetric Non-metric Connection Satisfying the Schur`s Theorem on a Riemannian Manifold

TL;DR

This paper investigates a new type of semi-symmetric non-metric connection on Riemannian manifolds that satisfies Schur's theorem, providing conditions under which the manifold has constant curvature.

Contribution

It introduces and studies properties of a semi-symmetric non-metric connection satisfying Schur's theorem, extending previous concepts in Riemannian geometry.

Findings

Characterization of conditions for constant curvature

Necessary and sufficient conditions for the connection

Extension of Schur's theorem to new connection types

Abstract

In 1992, Agache and Chaple introduced the concept of a semi-symmetric non-metric connection([1]). The semi-symmetric non-metric connection does not satisfy the Schur`s theorem. The purpose of the present paper is to study some properties of a new semi-symmetric non-metric connection satisfying the Schur`s theorem in a Riemannian manifold. And we considered necessary and sufficient condition that a Riemannian manifold with a semi-symmetric non-metric connection be a Riemannian manifold with constant curvature.