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

We define a new type of semi-symmetric non-metric connection on a Riemannian manifold and established its existence. Further, we find some basic results of curvature tensor and Ricci tensor. It is proved that such connection on a Riemannian manifold is projectively invariant under certain conditions. We also studied some properties of submanifolds of the Riemannian manifolds with respect to the semi-symmetric non-metric connection. To validate our findings, we construct two non-trivial examples of 3-dimensional and 5-dimensional Riemannian manifold equipped with a semi-symmetric non-metric connection.