Riemannian Curvature of a Sliced Contact Metric Manifold

Abstract

Contact geometry become a more important issue in the mathematical world with the works which had done in the 19th century. Many mathematicians have made studies on contact manifolds, almost contact manifolds, almost contact metric manifolds and contact metric manifolds. Many different studies have been done and papers have been published on Sasaki manifolds, Kähler manifolds, the other manifold types and submanifolds of them. In our previous studies we get the characterization of indefinite Sasakian manifolds. In order to get the characterization of indefinite Sasakian manifolds, firstly we defined sliced contact metric manifolds and then we examined the features of them. As a result we obtain a sliced almost contact metric manifold which is a wider class of almost contact metric manifolds. Thus, we constructed a sliced which is a contact metric manifold on an almost contact metric manifold where the manifold is not a contact metric manifold. Sliced almost contact metric manifolds generalized the almost contact metric manifolds. Then, we study on the sliced Sasakian manifolds and the submanifolds of them. Moreover we analyzed some important properties of the manifold theory on sliced almost contact metric manifolds.In this paper we calculated the -sectional curvature and the Riemannian curvature tensor of the sliced almost contact metric manifolds. Hence we think that all these studies will accelerate the studies on the contact manifolds and their submanifolds.