A new classification for almost C(α)-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, X-1)Ze = 0, B(xi, X-1)P = 0 and B(xi, X-1)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.