CR-SUBMANIFOLDS OF A LORENTZIAN PARA-SASAKIAN MANIFOLD WITH A SEMI-SYMMETRIC METRIC CONNECTION

Year 2010, Volume: 39 Issue: 4, 489 - 496, 01.04.2010

Cihan Özgür Mobin Ahmad  abdul Haseeb

Abstract

We study CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a semi-symmetric metric connection. Moreover, we obtain integrability conditions of the distributions on CR-submanifolds.

Keywords

CR-submanifold , Lorentzian para-Sasakian manifold , Semi-symmetric metric connection , Integrability conditions of the distributions , 2000 AMS Classification: 53 D 12

CR-SUBMANIFOLDS OF A LORENTZIAN PARA-SASAKIAN MANIFOLD WITH A SEMI-SYMMETRIC METRIC CONNECTION

Abstract

References

• Bejancu, A. CR-submanifolds of a Kaehler manifold I, Proc. Am. Math. Soc. 69, 135–142, 1978. [2] Bejancu, A. Geometry of CR-submanifolds (D. Reidel Pub. Co., 1986).
• De, U. C. and Sengupta, A. K. CR-submanifolds of a Lorentzian para-Sasakian manifold, Bull. Malaysian Math. Sci. Soc. 23, 99–106, 2000.
• Friedmann, A., Schouten, J. A., Uber die Geometric der halbsymmetrischen Ubertragung, Math. Z. 21, 211–223, 1924.
• Kobayashi, M. CR-submanifolds of Sasakian manifold, Tensor (N.S.) 35, 297–307, 1981.
• Matsumoto, K. On a Lorentzian para-contact manifolds, Bull. of Yamagata Univ. Nat. Sci. 12, 151–156, 1989.
• Matsumoto, K. and Mihai, I. On a certain transformation in a Lorentzian para-Sasakian manifold, Tensor (N.S.) 47, 189–197, 1988.
• Mihai, I. and Rosca, R. On Lorentzian P -Sasakian manifolds, Classical Analysis, World Scientific Publ., Singapore, 155–169, 1992.
• Sat¯o, I. On a structure similar to the almost contact structure, Tensor (N.S.) 30 (3), 219– 224, 1976.
• Sat¯o, I. On a structure similar to almost contact structures II, Tensor (N.S.) 31 (2), 199–205, 1977. [11] Schouten, J A., Ricci calculus (Springer, 1954).
• Yano, K. On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15, 1579–1586, 1970.