A Study on Generalized Einstein Tensor for an Almost Pseudo-Ricci Symmetric Manifold

Yıl 2022, Cilt: 10 Sayı: 1, 103 - 107, 15.04.2022

Hülya Yılmaz Samiye Aynur Uysal

Öz

The object of the paper is to study the generalized Einstein tensor $G(X,Y)$ on almost pseudo-Ricci symmetric manifolds, $A(PRS)_{n}$. Considering the generalized Einstein tensor $G(X,Y)$ as conservative, cyclic parallel and Codazzi type, it is investigated the properties of such a manifold.

Anahtar Kelimeler

Almost pseudo-Ricci symmetric manifold, Generalized Einstein tensor, Torqued vector field, Conservative, Cyclic parallel, Codazzi tensor.

Kaynakça

• [1] Besse, A. L., Einstein manifolds, Springer-Verlag, Berlin, 1987.
• [2] Cartan, E., Sur une classe remarquable d’espaces de Riemannian, Bull. S.M. F., 54(1926), 214–264. (In France.)
• [3] Cherevko, Y., Berezovski, V. and Chepurna, O., Conformal mappings of Riemannian manifolds preserving the generalized Einstein tensor, 17th Conference on Applied Mathematics, APLIMAT 2018-Proceedings, (2018), 224-231.
• [4] Chaki, M. C., On pseudo symmetric manifolds, Analele S¸ t Ale. Univ. Al. I. Cuza Din Ias¸i., 33(1987), 53-58.
• [5] Chaki, M. C., On pseudo Ricci symmetric manifolds, Bulgar. J. Phys., 15(1988), 526-531.
• [6] Chaki, M. C. and Kawaguchi, T., On almost pseudo Ricci symmetric manifolds, Tensor N.S., 68(2007), 10-14.
• [7] Bang-Yen Chen, Rectifying submanifolds of Riemannian manifolds and torqued vector fields, Kragujevac Journal of Mathematics, 41(1) (2017), 93–103.
• [8] Bang-Yen Chen, Classification of torqued vector fields and its applications to Ricci solutions, Kragujevac Journal of Mathematics, 41(2) (2017), 239–250.
• [9] De, U. C. and Gazi, A. K., On conformally flat almost pseudo Ricci symmetric manifolds, Kyungpook Math. J., 49(2009), 507-520.
• [10] De, U. C. and Shaikh, A. A., Differential geometry of manifolds, Alpha Sciences, Oxford, 2009.
• [11] Deszcz, R. ,On Ricci-pseudosymmetric warped products, Demonstratio Math., 22(1989), 1053-1065.
• [12] Deszcz, R. ,On pseudosymmetric spaces, Bull. Belg. Math. Soc., Ser. A, 44(1992), 1-34.
• [13] Hicks, N. J., Notes on differential geometry, Affiliated East-West Press. Pvt. Ltd., 1969.
• [14] Gray, A. , Einstein-like manifolds which are not Einstein, Geom. Dedicata, 7(1998), 259-280.
• [15] Petrov, A. Z., New methods in the general theory of relativity, Izdat. “Nauka”, Moscow, 1966.
• [16] Petrovi´c, M. Z., Stankovi´c, M. S. and Peska, P., On conformal and concircular diffeomorphisms of Eisenhart’s generalized Riemannian spaces, Mathematics, 626(7)(2019), doi:10.3390/math7070626.
• [17] Roter, W., On Conformally symmetric Ricci-recurrent spaces, Colloq. Math., 31(1974), 87–96.
• [18] Shaikh, A. A., Deszcz, R., Hotlos, M., Jelowicki, J. and Kundu, H., On pseudo symmetric manifolds, ArXiv: 1405.2181v2[math-DG], 27 June 2015.