CR-SUBMANIFOLDS OF A NEARLY -LORENTZIAN TRANS SASAKIAN MANIFOLD

Abstract

This paper considers the study of CR-submanifold of a nearly -Lorentzian trans Sasakian manifold, generalizing the results of a nearly -Lorentzian trans Sasakian manifold and thus those of Sasakian manifolds. We also obtain some results on parallel distribution relating to -vertical CR-submanifold of a nearly -Lorentzian trans Sasakian manifold.

Keywords

• CR-submanifold,nearly Lorentzian para-Sasakian manifold and -vertical CR-submanifold.

References

1. Bejancu, A., (1986), Geometry of CR-submanifolds, D. Reidel Publ. Co.
2. Bejancu, A., (1978) CR-submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. 69 (1) pp.135- 142.
3. Mihai, I. and Rosca, R., (1992), On Lorentzian P -Sasakian manifolds, Classical Analysis, World Scientific Publ., pp. 155-169.
4. Matsumoto, K., (1989) On Lorentzian para-contact manifolds, Bull. of Yamagata Univ.,Nat. Sci., 12, pp. 151-156.
5. Matsumoto, K. and Mihai, I., (1988), On a certain transformation in Lorentzian para-Sasakian man- ifold, Tensor, N.S., 47, pp. 189-197.
6. Yano K. and Kon, M.,(1982) Contact CR-submanifolds, Kodai Math. J. 5 (2), pp. 238-252.
7. Duggal K. L. and Bejancu, A.,(1994) Spacetime geometry of CR-structures, Contemporary Math. 170, pp. 49-63.
8. Kobayashi, M. (1981) CR-submanifolds of a Sasakian manifold, Tensor, N.S., 35 (3), pp. 297-307.

9. Shahid, M. H. , Sharfuddin, A. and Husain, S. A.,(1985) CR-submanifolds of a Sasakian manifold, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 15 (1), pp. 263-278.
10. De, U.C., Matsumoto K. and Shaikh, A. A., (1999), On Lorentzian para-Sasakian manifolds, Rendicontidel Seminario Matematico di Messina, Serie II, Supplemento al n., 3, pp.149-158.