A note on almost $C(\alpha)-$ manifolds
Authors :
Halil Ibrahim Yoldas
Author Address :
1 Department of Mathematics, Faculty of Science and Arts, Mersin University, 33343, Mersin, Turkey.
Abstract :
In this paper, we concentrate on almost $C(\alpha)-$ manifolds. Firstly, we study almost $C(\alpha)-$ manifolds satisfying the curvature conditions $R.Q=0$, $R(\xi,X).\mathcal{Z}=0$ and $R(\xi,X).R=0$, where $\mathcal{Z}$ is the curvature tensor of type $(0,2)$, $R$ is the Riemannian curvature tensor and $Q$ is the Ricci operator. Then, we deal with $\mathcal{Z}-$ recurrent and generalized Ricci recurrent $C(\alpha)-$ manifolds and give an important relationship between such manifolds.
Keywords :
Almost $C(\alpha)-$manifold, Einstein Manifold, Generalized Ricci recurrent manifold, $\mathcal{Z}-$curvature tensor.
DOI :
Article Info :
Received : February 15, 2020; Accepted : August 09, 2020.
