# CERTAIN CURVATURE CONDITIONS ON AN LP-SASAKIAN MANIFOLD WITH A COEFFICIENT α

• De, Uday Chand ;
• Published : 2009.05.31
• 64 5

#### Abstract

The object of the present paper is to study certain curvature restriction on an LP-Sasakian manifold with a coefficient $\alpha$. Among others it is shown that if an LP-Sasakian manifold with a coefficient $\alpha$ is a manifold of constant curvature, then the manifold is the product manifold. Also it is proved that a 3-dimensional Ricci semisymmetric LP-Sasakian manifold with a constant coefficient $\alpha$ is a spaceform.

#### Keywords

Lorentzian Para-Sasakian manifold with a coefficient $\alpha$;manifold of constant curvature

#### References

1. T. Adati and A. Kandatu, On hypersurfaces of P-Sasakian manifolds and manifolds admitting a concircular vector field, Tensor (N.S.) 34 (1980), no. 1, 97–102
2. F. Brickell and R. S. Clark, Differentiable Manifold, Van Nostrand Reinhold Comp. London 1978
3. U. C. De, A. A. Shaikh, and A. Sengupta, On LP-Sasakian manifolds with a coefficient $\alpha$, Kyungpook Math. J. 42 (2002), no. 1, 177–186
4. T. Ikawa and M. Erdogan, Sasakian manifolds with Lorentzian metric, Kyungpook Math. J. 35 (1996), no. 3, Special Issue, 517–526
5. T. Ikawa and J. B. Jun, On sectional curvatures of a normal contact Lorentzian manifold, Korean J. Math. Sci. 4 (1997), 27–33
6. K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci. 12 (1989), no. 2, 151–156
7. L. Verstraelen, Comments on pseudo-symmetry in the sense of Ryszard Deszcz, Geometry and topology of submanifolds, VI (Leuven, 1993/Brussels, 1993), 199–209, World Sci. Publ., River Edge, NJ, 1994
8. K. Yano, On the torse-forming directions in Riemannian spaces, Proc. Imp. Acad. Tokyo 20 (1944), 340–345 https://doi.org/10.3792/pia/1195572958
9. I. Mihai and R. Rosca, On Lorentzian P-Sasakian manifolds, Classical analysis (Kazimierz Dolny, 1991), 155–169, World Sci. Publ., River Edge, NJ, 1992

#### Cited by

1. Warped product CR-submanifolds of LP-cosymplectic manifolds vol.24, pp.1, 2010, https://doi.org/10.2298/FIL1001087U