Browse > Article
http://dx.doi.org/10.7468/jksmeb.2017.24.2.53

ON GENERALIZED Z-RECURRENT MANIFOLDS  

De, Uday Chand (Department of Pure Mathematics, University of Calcutta)
Pal, Prajjwal (Chakdaha Co-operative Colony Vidyayatan(H.S))
Publication Information
The Pure and Applied Mathematics / v.24, no.2, 2017 , pp. 53-68 More about this Journal
Abstract
The object of the present paper is to study generalized Z-recurrent manifolds. Some geometric properties of generalized Z-recurrent manifolds have been studied under certain curvature conditions. Finally, we give an example of a generalized Z-recurrent manifold.
Keywords
generalized Ricci-recurrent manifolds; generalized Z-recurrent manifolds; quasi Einstein manifolds;
Citations & Related Records
연도 인용수 순위
  • Reference
1 T. Adati & T. Miyazawa: On a Riemannian space with recurrent conformal curvature. Tensor(N.S.) 18 (1967), 348-354.
2 K. Arslan, U.C. De, C. Murathan & A. Yildiz: On generalized recurrent Riemannian manifolds. Acta Math. Hungarica 123 (2009), 27-39.   DOI
3 E. Cartan: Sur une classes remarquable d'espaces de Riemannian. Bull. Soc. Math. France, 54 (1926), 214-264.
4 M.C. Chaki: Some theorems on recurrent and Ricci-recurrent spaces. Rendiconti Seminario Math. Della Universita Di Padova 26 (1956), 168-176.
5 M.C. Chaki & B. Gupta: On conformally symmetric spaces. Indian J. Math. 5 (1963), 113-122.
6 M.C. Chaki: On pseudo symmetric manifolds. Ann. St. Univ. "Al I Cuza" Iasi 33 (1987), 53-58.
7 M.C. Chaki: On pseudo Ricci symmetric manifolds. Bulg. J. Phys. 15 (1988), 525-531.
8 M.C. Chaki & S.K. Saha: On pseudo-projective Ricci symmetric manifolds. Bulg. J. Phys. 21 (1994), 1-7.
9 B.Y. Chen & K. Yano: Hypersurfaces of a conformally flat spaces. Tensor, N. S. 26 (1972), 318-322.
10 S.S. Chern: On the curvature and characteristic classes of a Riemannian manifold. Abh. Math. Sem. Univ. Hamburg 20 (1956), 117-126.
11 U.C. De & A.K. Gazi: On generalized concircularly recurrent manifolds. Studia Sci. Math. Hungar 46 (2009), no. 2, 287-296.   DOI
12 U.C. De, N. Guha & D. Kamilya: On generalized Ricci-recurrent manifolds. Tensor(N.S.) 56 (1995), 312-317.
13 L.P. Eisenhart: Riemannian Geometry. Princeton University Press, 1949.
14 D. Ghosh: On projective recurrent spaces of second order. Acad. Roy. Belg. Bull. Cl. Sci. 56 (1970), no. 5, 1093-1099.
15 A. Lichnerowicz: Courbure, nombres de Betti, et espaces symmetriques. Proc. Int. Cong. Math. 2 (1950), 216-233.
16 S. Mallick, A. De & U.C. De: On generalized Ricci recurrent manifolds with applications to relativity. Proc. Nat. Acad. Sci., India, Sect. A Phys. Sci. 83 (2013), 143-152.   DOI
17 C.A. Mantica & Y.J. Suh: Conformally symmetric manifolds and quasi-conformally recurrent Riemannian manifolds. Balkan J. Geom. Appl. 16 (2011), 66-67.
18 C.A. Mantica & L.G. Molinari: Weakly Z-Symmetric manifolds. Acta Math. Hungarica 135 (2012), 80-96.   DOI
19 C.A. Mantica & Y.J. Suh: Pseudo-Z-symmetric Riemannian manifolds with harmonic curvature tensors. Int. J. Geom. Meth. Mod. Phys. 9 (2012) 1250004(21 pages).
20 C.A. Mantica & Y.J. Suh: Recurrent Z forms on Riemannian and Kaehler manifolds. Int. J. Geom. Meth. Mod. Phys. 9 (2012) 1250059(26 pages).
21 B. O'Neill: Semi-Riemannian Geometry with Applications to the Relativity. Academic Press, New York-London, 1983.
22 E.M. Patterson: Some theorems on Ricci-recurrent spaces. J. London. Math. Soc. 27 (1952), 287-295.
23 C. Ozgur: On generalized recurrent Kenmotsu manifolds. World Applied Sciences Journal 2 (2007), 9-33.
24 C. Ozgur: On generalized recurrent contact metric manifolds Indian J. Math. 50 (2008), 11-19.
25 C. Ozgur: On generalized recurrent Lorentzian para-Sasakian manifolds. Int. J. Appl. Math. Stat. 13 (2008), 92-97.
26 N. Prakash: A note on Ricci-recurrent and recurrent spaces. Bull. Cal. Math. Society 54 (1962), 1-7.
27 W. Roter: On conformally symmetric Ricci-recurrent spaces. Colloquium Mathematicum. 31 (1974), 87-96.   DOI
28 J.A. Schouten: Ricci-Calculus. An introduction to Tensor Analysis and its Geometrical Applications. Springer-Verlag, Berlin-Gottingen-Heidelberg, 1954.
29 L. Tamassy & T.Q. Binh: On weakly symmetries of Einstein and Sasakian manifolds: Tensor (N.S.). 53 (1993), 140-148.
30 A.G. Walker: On Ruse's space of recurrent curvature. Proc. of London Math. Soc., 52 (1950), 36-54.
31 S. Yamaguchi & M. Matsumoto: On Ricci-recurrent spaces. Tensor, N. S. 19 (1968), 64-68.
32 K. Yano & M. Kon: Structures on manifolds. World scientific, Singapore, 1984, 418-421.