Einstein like -para Sasakian manifolds



Einstein like  -para Sasakian manifolds are introduced. For an  -para Sasakian manifold to be Einstein like, a necessary and sufficient condition in terms of its curvature tensor is obtained. The scalar curvature of an Einstein like  -para Sasakian manifold is obtained and it is shown that the scalar curvature in this case must satisfy certain differential equation. A necessary and sufficient condition for an  -almost paracontact metric hypersurface of an indefinite locally Riemannian product manifold to be  -para Sasakian is obtained and it is proved that the  -para Sasakian hypersurface of an indefinite locally Riemannian product manifold of almost constant curvature is always Einstein like.


Einstein like -para Sasakian manifold; indefinite locally Riemannian product manifold.

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Beem, J. K. & Ehrlich, P. E. 1981 . Global Lorentzian geometry. Marcel Dekker, New York.

Bejancu, A. & Duggal, K. L. 1993 . Real hypersurfaces of indefinite Kaehler manifolds<$>. International Journal of Mathematics and Mathematical Sciences 16 (3): 545-556.

Blair, D. E. 2002 . Riemannian geometry of contact and symplectic manifolds. Progress in Mathematics (203). Birkhauser Boston, Inc., Boston, MA.

Chen, B.-Y. 1973 . Geometry of submanifolds. Pure and Applied Mathematics (22). Marcel Dekker, New York.

Duggal, K. L. 1990 . Space time manifolds and contact structures. International Journal of Mathematics and Mathematical Sciences 13 : 545-554.

Matsumoto, K . 1989. On Lorentzian paracontact manifolds. Bulletin of Yamagata University Natural Science 12 (2): 151-156.

O'Neill, B. 1983 . Semi-Riemannian geometry with applications to relativity<$>,<$> Academic Press.

Sasaki, S. 1960 . On differentiable manifolds with certain structures which are closely related to almost contact structure I. Tohoku Mathematical Journal 12 (2): 459-476.

Sato, I. 1976 . On a structure similar to the almost contact structure. Tensor (NS) 30 (3): 219-224.

Sharma, R. 1982 . On Einstein-like P-Sasakian manifold, Matematicki Vesnik 6 (19)(34) (2): 177-184.

Takahashi, T. 1969 . Sasakian manifold with pseudo-Riemannian metric<$>,<$> T^‡‡‡‡‡‡‡‡‡‡‡ohoku Mathematical Journal 21 (2): 644-653.

Tripathi, M. M., Kilõõiµ, E., Perkta<?tlig="lig">_s, S. Y. & Kele<?tlig="lig">_s, S. 2010 . Indefinite almost paracontact metric manifolds, International Journal of Mathematics and Mathematical Sciences. pp. 19.

Yano, K. 1965 . Differential geometry on complex and almost complex spaces, International Series of Monographs in Pure and Applied Mathematics (49) A Pergamon Press Book. The Macmillan Coorporation, New York.


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