Riemannian manifolds admitting a new type of semi-symmetric non-metric connection

Abstract

In this paper, we define a semi-symmetric non-metric connection Dഥ on a Riemannian manifold M and proved its existence. In particular cases, this connection reduces to several symmetric, semi-symmetric and semi-symmetric non-metric connections; even some of them are not introduced so for. We also find the expression for curvature tensor, Ricci tensor and scalar curvature of this new connection Dഥ. Further, it is also proved that such connection on a Riemannian manifold is conformally and projectively invariant under certain conditions. Also we study a hypersurface of a Riemannian manifold admitting such a semisymmetric non-metric connection. To validate our findings, we construct a non-trivial example of 3– dimensional Riemannian manifold equipped with a semi-symmetric non-metric connection.