1912

On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds

In the present work, generalized recurrent and generalized concircularly recurrent Weylmanifolds are examined. Nearly quasi-Einstein Weyl manifolds are defined and it is proved thatif a generalized recurrent or generalized concircularly recurrent Weyl manifold admits a specialconcircular vector field, then the manifold is a nearly quasi-Einstein Weyl manifold. Also, someother results are presented.

PDF

___

[1] H. Weyl, “Raum-Zeit-Materie”, J. Springer, 1918.

[2] A. G. Walker, “On Ruse's spaces of recurrent curvature,” Proc. Lond. Math., vol. 52, pp. 34-36, 1951.

[3] U. C. De and N. Guha, “On generalized recurrent manifolds,” J. National Academy of Math. India, vol. 9, pp. 85-92, 1991.

[4] K. Arslan, U. C. De, C. Murathan and A. Yıldız, “On generalized recurrent Riemannian manifolds,” Acta Math. Hungar., vol. 123 (1-2), pp. 27-39, 2009.

[5] T. Miyazawa, “On Riemannian space admitting some recurrent tensor,” Tru. Math. J., vol.2, pp. 11-18, 1996.

[6] U. C. De and A. K. Gazi, “On generalized concircularly recurrent manifolds,” Studia Scient. Math. Hungar., vol. 46(2), pp. 287- 296, 2009.

[7] E. M. Patterson, “Some theorems on Riccirecurrent spaces,” J. Lond. Math. Soc., vol. 27, pp. 287–295, 1952.

[8] U. C. De, N. Guha and D. Kamilya, “On generalized Ricci recurrent manifolds,” Tensor (NS), vol. 56, pp. 312–317, 1995.

[9] A. A. Shaikh, I. Roy and H. Kundu, “On some generalized recurrent manifolds”, Bull. Iranian Math. Soc., vol. 43(5), pp. 1209-1225, (2017).

[10] S. A. Uysal and H. B. Yılmaz, "Some Properties of Generalized Einstein Tensor for a Pseudo-Ricci Symmetric Manifold," Advances in Mathematical Physics, vol. 2020, Article ID 6831650, 4 pages, 2020.

[11] J. Kim, “On Almost Quasi Ricci Symmetric Manifolds,” Commun. Korean Math. Soc. Vol. 35, No. 2, pp. 603-611, 2020.

[12] E. Canfes, “On Generalized Recurrent Weyl Spaces and Wong's Conjecture,” Differential Geometry and Dynamical Systems, vol. 8, pp. 34-42, 2006.

[13] G. Gürpınar Arsan, G. Çivi Yıldırım, “Generalized concircular recurrent Weyl spaces,” Proceedings of the 4th International Colloquium Mathematics in Engineering and Numerical Physics, pp. 6- 8, 2006.

[14] U. C. De and A. K. Gazi, “On nearly quasi Einstein manifolds,” Novi Sad. J. Math., vol. 38(2), pp. 115–121, 2008.

[15] V. Hlavaty, “Theorie d'immersion d'une ?? dans ??,” Ann. Soc. Polon. Math., vol. 21, pp. 196-206, 1949.

[16] A. Norden, “Affinely Connected Spaces,” Nauka, Moscow, 1976.

[17] G. Zlatanov, “Nets in the n-dimensional Space of Weyl,” C. R. Aoad. Bulgare Sci., vol. 41, no. 10, pp 29-32, 1988.

[18] A. Özdeğer, “On sectional curvatures of Weyl manifolds,” Proc. Japan Acad, vol. 82A, no. 8, pp. 123-125, 2006.

[19] A. Özdeğer and Z. Şentürk, “Generalized Circles in Weyl spaces and their conformal mapping,” Publ. Math. Debrecen, vol. 60, no. 1-2, pp. 75-87, 2002.