Some Curvature Conditions Provided by the Projective Curvature Tensor on the Almost C(α)-Manifold
Projective Curvature Tensor on the Almost C(α)-Manifold
Resumo
In this article, the projective curvature tensor on a C(α)-manifold is discussed. Some special curvature conditions provided by the projective curvature tensor on the Riemann, Ricci, concircular curvature tensors have been investigated. As a result of the curvature conditions given with the projective curvature tensor on a C(α)-manifold, cases such as the (2n+1)-dimensional manifold being Einstein and η-Einstein manifolds have been characterized.
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Referências
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12 : Mert, T., Atçeken, M., Almost C(α)-manifold on W₀^{∗}-Curvature Tensor, Applied Mathematical Sciences, 15 (2020), 693-703.
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2 : Szabo, Z. I., Structure theorems on riemannian spaces satisfying R(X,Y)R=0, I: The local Version, J. Differential Geom., 17 (1982), 531-582.
3 : Takahashi, T., Sasakian φ-symmetric spaces, Tohoku Math. J., 29 (1977), 91-113.
4 : De, U.C.,Sarkar, A., On the Projective curvature tensor of generalized Sasakian space forms, Questiones Mathematicae, 33 (2010), 245-252.
5 : Yıldırım, U., Atçeken, M., Dirik, S.,Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold, Commun. Fac. Sci. Univ. Ank. Ser. A1, Math. Stat. 68 (2019)997-1006.
6 : Chaubey, S. K., Some properties of Lp-Sasakian manifolds equipped with M-projective curvature tensor, Bulletin of Mathematical Analysis and Applications, 3 (2011), 50-58.
7 : Vankatesha, B. Sumangala, On M-projective curvature tensorof a generalized Sasakian space form, Acta Math. Univ. Comenianae, 2 (2013), 209-217.
8 : Yıldız, A., De, U.C., Murathan C., Arslan K., On the weyl projective curvature tensor of an N(k)-contact metric manifold, Mathematica Pannonica, 21 (2010), 1-14.
9 : Atçeken, M., On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor, Bulletin of Mathematical Analysis and Applications, 6 (2014), 1-8.
10 : Özgür, C., De, U.C., On the quasi-conformal curvature tensor of a Kenmotsu manifold, Mathematica Pannonica, 17 (2006), 221-228.
11 : Chaubey, S. K., Prakash, S., Nivas, R., Some properties of M-projective curvature tensor in Kenmotsu manifolds, Bulletin of Mathematical Analysis and Applications, 4 (2012), 48-56.
12 : Mert, T., Atçeken, M., Almost C(α)-manifold on W₀^{∗}-Curvature Tensor, Applied Mathematical Sciences, 15 (2020), 693-703.
13 : Yano,K., Sawaki, S., Riemann manifolds admitting a conformal transformation group, J. Diff. Geom., 2 (1968), 161-184.
14 : Yano, K., Concircular geometry I. concircular transformations, Proc. ımp. acad., Tokyo, 16 (1940), 195-200.
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2025-11-01
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