On Almost C(α)-Manifold Satisfying Certain Curvature Conditions

Abstract

This research article is about the geometry of the almost C(α)- manifold. Some important properties of the almost C(α)- manifold with respect to the W_3- curvature tensor, such as W_3-flat and W_3- semi-symmetry, are investigated. The relationship of W_3- curvature tensor with Riemann, Ricci, projective, concircular and quasi-conformal curvature tensor is discussed on the almost C(α)- manifold and many important results are obtained. In addition, W_3- pseudo symmetry and W_3- Ricci pseudo symmetry are investigated for the almost C(α)- manifold. The results obtained are interesting and give an idea about the geometry of the almost C(α)- manifold.