On Generalized Pseudo-Projectively Recurrent Manifolds


Affiliations

  • Mizoram University, Department of Mathematics and Computer Science, Tanhril, Aizawl, India
  • Mizoram University, Department of Mathematics and Computer Science, Tanhril, Aizawl, 796004, India

Abstract

The object of the present paper is to study generalized pseudo-projectively recurrent manifolds. Some geometric properties of generalized pseudo-projectively recurrent manifolds have been studied under certain curvature conditions. Finally the existence of generalized pseudo-projectively recurrent manifold is shown by examples.


Keywords

Pseudo-projectively Recurrent Manifolds, Generalized Pseudo-projectively recurrent manifolds, Ricci Symmetric Manifolds, Product Manifolds

Full Text:

References

T. Adati and T. Miyazawa, On Riemannian space with recurrent conformal curvature, Tensor (N.S.) 18 (1967), 348-354.

K. Arslan, U.C. De, C. Murathan and A. Yildiz, On generalized recurrent Riemannian manifolds, Acta Math. Hungar. 123 (2009), 27-39.

E. Cartan, Sur une classe remarquable despaces de Riemann, Bull. Soc. Math. France 54 (1926), 214-264.

M. C. Chaki, Some theorems on recurrent and Ricci-recurrent spaces, Rend. Sem. Mat. Univ. Padova 26 (1956), 168-76.

M. C. Chaki and B. Gupta, On conformally symmetric spaces, Indian J. Math. 5 (1963), 113-122.

M. C. Chaki, On pseudo symmetric manifolds, An. Stiint. Univ. `Al. I. Cuza' Iasi Sect. I a Mat. 3 (1987), 53-58.

U. C. De and A. K. Gazi, On almost pseudo conformally symmetric manifolds, Demonstratio Mathematica 42 (2009), 869-886.

U.C. De, N. Guha, On generalised recurrent manifolds, Proc. Math. Soc. 7 (1991), 7-11.

U. C. De, N. Guha and D. Kamilya, On generalized Ricci-recurrent manifolds, Tensor (N.S.) 56 (1995), 312-317.

U. C. De and P. Pal, On generalised M-projectively recurrent manifolds, Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica 13 (2014), 77-101.

L. P. Eisenhart, , Riemannian Geometry, 2nd printing, Princeton University Press, Princeton, N. J., 1949.

D. Ghosh, On projective recurrent spaces of second order, Acad. Roy. Belg. Bull. Cl. Sci. 5 (1970), 1093-1099.

S. Guler and S. A. Demirbag, Riemannian Manifolds Satisfying Certain Conditions on Pseudo-Projective Curvature Tensor, Filomat 30 (2016), 721-731.

P. Gupta, Index of pseudo-projectively symmetric semi-Riemannian manifolds, Carpathian Math. Publ. 7 (2015), 57-65.

M. Hotlos, On conformally symmetric warped products, Ann. Acad. Pedagog. Crac. Stud. Math. 4 (2004), 75-85.

G. I. Kruckovic, On semireducible Riemannian spaces, Dokl. Akad. Nauk SSSR (N.S.) 115 (1957), 862-865.

A. Lichnerowicz, Courbure, nombres de Betti, et espaces symtriques (French), Proceedings of the International Congress of Mathematicians, Cambridge, Mass. 2 (1950), 216-223.

S. Mallick, A. De and U. C. De, On generalized Ricci recurrent manifolds with applications to relativity, Proc. Nat. Acad. Sci. India Sect. A 83 (2013), 143-152.

Y. B. Maralabhavi and G. S. Shivaprasanna, On pseudo-projective curvature tensor in LP- Sasakian manifolds, Int. Math. Forum 7 (2012), 1121-1128.

H. G. Nagaraja and G. Somashekhara, on pseudo projective curvature tensor in Sasakian manifolds, Int. J. Contemp. Math. Sciences 6 (2011), 1319-1328.

C. Ozgur, On generalized recurrent Kenmotsu manifolds, World Appl. Sci. J. 2 (2007), 9-33.

C. Ozgur, On generalized recurrent contact metric manifolds, Indian J. Math. 50 (2008),11-19.

C. Ozgur, On generalized recurrent Lorentzian para-Sasakian manifolds, Int. J. Appl. Math. Stat. 13 (2008), 92-97.

E. M. Patterson, Some theorems on Ricci-recurrent spaces, J. London Math. Soc. 27 (1952),287-295.

N. Prakash, A note on Ricci-recurrent and recurrent spaces, Bull. Calcutta Math. Soc. 54(1962), 1-7.

B. Prasad, A pseudo-projective curvature tensor on a Riemannian manifolds, Bull. Cal. Math. Soc. 94 (2002), 163-166.

W. Roter, On conformally symmetric Ricci-recurrent spaces, Colloq. Math. 31 (1974), 87-96.

W. Roter, On conformally recurrent Ricci-recurrent manifolds, Colloq. Math. 46 (1982),45-57.

H.S. Ruse, A classication of K*-spaces, Proc. London Math. Soc. 53 (1951), 212-229.

J. A. Schouten, Ricci-calculus. An introduction to tensor analysis and its geometrical applications, 2d. ed. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Bercksichtigung der Anwendungsgebiete, Bd X. Springer-Verlag, Berlin-Gttingen-Heidelberg, 1954.

L. Tamassy and T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Colloq. Math. Soc. Jnos Bolyai 56 (1989), 663-670.

A. G. Walker, On Ruses spaces of recurrent curvature, Proc. London Math. Soc. 52 (1950),36-64.

S. Yamaguchi and M. Matsumoto, On Ricci-recurrent spaces,Tensor (N.S.) 19 (1968), 64-68.

K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics 3, World Scientic

Publishing Co., Singapore, 1984.


Refbacks

  • There are currently no refbacks.