Some Properties of a Kenmotsu manifold with a semi-symmetric metric connection

Year 2010, Volume: 3 Issue: 1, 24 - 34, 30.04.2010

Sibel Sular

Abstract

 

Keywords

Kenmotsu manifold, semi-symmetric metric connection, generalized recurrent manifold, generalized Ricci-recurrent manifold, weakly symmetric manifold, weakly Ricci-symmetric manifold

References

• [1] D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics 203, Birkhouser Boston, Inc., MA, 2002.
• [2] M. C. Chaki, On pseudo symmetric manifolds, An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 33 (1987), no. 1, 53–58.
• [3] M. C. Chaki, On pseudo Ricci symmetric manifolds, Bulgar. J. Phys. 15 (1988), no. 6, 526–531.
• [4] U. C. De, N. Guha, On generalised recurrent manifolds, Proc. Math. Soc. 7 (1991), 7-11.
• [5] U. C. De, G. Pathak, On a semi-symmetric metric connection in a Kenmotsu manifold, Bull. Calcutta Math. Soc. 94 (2002), no. 4, 319–324.
• [6] A. Friedmann and J. A. Schouten, Über die Geometrie der halbsymmetrischen Übertragungen, Math. Z. 21 (1924), no. 1, 211–223.
• [7] H. A. Hayden, Subspace of a space with torsion, Proceedings of the London Mathe- matical Society II Series 34 (1932), 27-50.
• [8] T. Imai, Notes on semi-symmetric metric connections, Vol. I. Tensor (N.S.) 24 (1972), 293–296.
• [9] T. Imai, Hypersurfaces of a Riemannian manifold with semi-symmetric metric con- nection, Tensor (N.S.) 23 (1972), 300–306.
• [10] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. Journ. 24(1972), 93-103.
• [11] C. Özgür, On weakly symmetric Kenmotsu manifolds, Differ. Geom. Dyn. Syst. 8 (2006), 204–209.
• [12] C. Özgür, On generalized recurrent Kenmotsu manifolds, World Applied Sciences Journal 2 (2007), no.1, 29-33.
• [13] A. Sharfuddin and S. I. Husain, Semi-symmetric metric connexions in almost contact manifolds, Tensor(N.S.) 30 (1976), no. 2, 133–139.
• [14] L. Tamássy, T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Colloq. Math. Soc. J. Bolyai, 56 (1992), 663–670.
• [15] L. Tamássy, T. Q. Binh, On weak symmetries of Einstein and Sasakian mani- folds,Tensor (N.S.) 53 (1993), no.1, 140–148.
• [16] M. M. Tripathi, On a semi symmetric metric connection in a Kenmotsu manifold, J. Pure Math. 16 (1999), 67–71.
• [17] K. Yano, On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.
• [18] A. Yücesan, On semi-Riemannian submanifolds of a semi-Riemannian manifold with a semi-symmetric metric connection, Kuwait J. Sci. Eng. 35 (2008), no. 1A, 53–69.