A New Classification of Almost C(\alpha)-Manifolds

Abstract

In this paper, D-conformal curvature tensor on an almost
C(\alpha)-manifold has been considered. At first, a few fundamental geometric properties of D-conformal curvature tensor on an almost C(\alpha)-manifold have been obtained with some interesting outcomes. Moreover, the necessary and sufficient conditions have been addressed for almost C(\alpha)-manifold to be D-conformally flat, D-conformally semi-symmetric, B(\xi,Y)\widetilde{Z}=0, B(\xi,Y)P=0 and B(\xi,Y)S=0. It is shown that a D-Conformal flat C(\alpha) manifold reduces to the Kenmotsu manifold and a D-Conformal Semi Symmetric C(\alpha) manifold reduces to the co-Keahler manifold. At the end, an example of an almost C(\alpha) manifold has been presented.