A note on almost \(C(\alpha)\)- manifolds
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https://doi.org/10.26637/MJM0804/0003Abstract
In this paper, we concentrate on almost \(C(\alpha)\) - manifolds. Firstly, we study almost \(C(\alpha)\) - manifolds satisfying the curvature conditions \(R \cdot Q=0, R(\xi, X) \cdot \mathscr{Z}=0\) and \(R(\xi, X) \cdot R=0\), where \(\mathscr{Z}\) is the curvature tensor of type \((0,2), R\) is the Riemannian curvature tensor and \(Q\) is the Ricci operator. Then, we deal with \(\mathscr{Z}\) - recurrent and generalized Ricci recurrent \(C(\alpha)\) - manifolds and give an important relationship between such manifolds.
Keywords:
Einstein Manifold, Generalized Ricci recurrent manifold, Z-curvature tensor, Almost \(C(\alpha)\)-manifoldMathematics Subject Classification:
Mathematics- Pages: 1358-1362
- Date Published: 01-10-2020
- Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
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