Riemannian manifolds admitting a new type of semisymmetric nonmetric connection

Abstract

We define a new type of semisymmetric nonmetric connection on a Riemannian manifold and establishits existence. It is proved that such connection on a Riemannian manifold is projectively invariant under certainconditions. We also find many basic results of the Riemannian manifolds and study the properties of group manifoldsand submanifolds of the Riemannian manifolds with respect to the semisymmetric nonmetric connection. To validateour findings, we construct a nontrivial example of a 3-dimensional Riemannian manifold equipped with a semisymmetricnonmetric connection.