Geodesic
On a generalized class of recurrent manifolds
Archivum mathematicum, Tome 46 (2010) no. 1, pp. 71-78 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The object of the present paper is to introduce a non-flat Riemannian manifold called hyper-generalized recurrent manifolds and study its various geometric properties along with the existence of a proper example.
The object of the present paper is to introduce a non-flat Riemannian manifold called hyper-generalized recurrent manifolds and study its various geometric properties along with the existence of a proper example.
Classification : 53B35, 53B50
Keywords: recurrent; generalized recurrent; conharmonically recurrent; hyper-generalized recurrent; generalized conharmonically recurrent; generalized Ricci recurrent manifold 
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Shaikh, Absos Ali; Patra, Ananta. On a generalized class of recurrent manifolds. Archivum mathematicum, Tome 46 (2010) no. 1, pp. 71-78. http://geodesic.mathdoc.fr/item/ARM_2010_46_1_a5/

[1] Adati, T., Miyazawa, T.: On Riemannian space with recurrent conformal curvature. Tensor (N.S.) 18 (1967), 348–354. | MR

[2] Adati, T., Miyazawa, T.: On projective transformations of projective recurrent spaces. Tensor (N.S.) 31 (1977), 49–54. | MR | Zbl

[3] Arslan, K., De, U. C., Murathan, C., Yildiz, A.: On generalized recurrent Riemannian manifolds. Acta Math. Hungar. 123 (2009), 27–39. | DOI | MR | Zbl

[4] De, U. C., Guha, N., Kamilya, D.: On generalized Ricci recurrent manifolds. Tensor (N.S) 56 (1995), 312–317. | MR | Zbl

[5] Ishii, Y.: On conharmonic transformations. Tensor ( N.S.) 11 (1957), 73–80. | MR | Zbl

[6] Lichnerowicz, A.: Courbure, nombres de Betti, et espaces symmetriques. Proc. of the Intern. Congress of Math., vol. 2, 1952, pp. 216–223. | MR

[7] Miyazawa, T.: On Riemannian space admitting some recurrent tensor. TRU Math. J. 2 (1996), 11–18. | MR

[8] Patterson, E. M.: Some theorems on Ricci recurrent spaces. J. London. Math. Soc. 27 (1952), 287–295. | DOI | MR | Zbl

[9] Shaikh, A. A., Jana, S. K.: On weakly cyclic Ricci symmetric manifolds. Ann. Polon. Math. 89 (3) (2006), 273–288. | DOI | MR | Zbl

[10] Tamássy, L., Binh, T. Q.: On weakly symmetric and weakly projective symmetric Riemannian manifolds. Colloq. Math. Soc. János Bolyai 56 (1989), 663–670. | MR

[11] Tamássy, L., Binh, T. Q.: On weak symmetries of Einstein and Sasakian manifolds. Tensor (N.S.) 53 (1993), 140–148. | MR

[12] Walkar, A. G.: On Ruse’s spaces of recurrent curvature. Proc. London Math. Soc. 52 (1950), 36–64. | MR

[13] Yano, K.: Concircular geometry I. Proc. Imp. Acad. Tokyo 16 (1940), 195–200. | MR