Abstract

In this paper, we study projective curvature tensor on 3-dimensional LP-Sasakian manifolds. Mainly, we consider projectively semisymmetric and f -projectively semisymmetric 3- dimensional LP-Sasakian manifolds and it is proved that in both the situations the manifold is infinitesimally spatially isotropic relative to the unit timelike vector field x .

References

[1] A. A. Aqueel, U. C. De, G. C. Ghosh, On Lorentzian Para-Sasakian manifolds, Kuwait J. Sci. Eng., 31(2) (2004), 1-13.
[2] U. C. De, K. Matsumoto and A.A. Shaikh, On Lorentzian Para-Sasakian manifolds, Rend. Semin. Mat. Messina, 3 (1999), 149-156.
[3] H. Karcher, Infinitesimal characterization of Friedman universe, Arch. Math. (Basel), 38 (1982) 58-64.
[4] K. Matsumoto, On Lorentzian Para contact manifolds, Bull. of Yamagata Univ., Nat. Sci., 12 (1989) 151-156.
[5] I. Mihai, R. Rosca, On Lorentzian Para-Sasakian Manifolds, Class. Anal, World Sci. Publ., Singapore, (1992), 155-169.
[6] I. Mihai, U. C. De, A. A. Shaikh, On Lorentzian Para-Sasakian Manifolds, Korean J. Math. Sci., 6 (1999), 1-13.
[7] R. S. Mishra, Structures on Differentiable Manifold and Their Applications, Chandrama Prakasana, Allahabad, 1984.
[8] C. Murathan, A. Yildiz, K. Arslan, U. C. De, On a class of Lorentzian Para-Sasakian manifolds, Proc. Estonian Acad. Sci. Phys. Math., 55(4) (2006), 210-219.
[9] Y. A. Ogawa, Condition for a compact Kahlerian space to be locally symmetric, Natur. Sci. Report, Ochanomizu Univ., 28 (1971), 21.
[10] A. A. Shaikh, K. K. Baishya, Some results on LP-Sasakian manifolds, Bull. Math. Sci. Soc., 49 (97)(2) (2006), 193 - 205.

[11] A. A. Shaikh, K. K. Baishya, On  -symmetric LPSasakian manifolds, Yokohama Math. J., 52 (2005), 97 - 112.

[12] A. A. Shaikh, D. G. Prakasha, H. Ahmad, On generalized  -recurrent LP-Sasakian manifolds, J. Egyptian Math. Soc. 23 (2015,) 161-166.

[13] A. A. Shaikh and U. C. De, On 3-dimensional LP-Sasakian manifolds, Soochow J. Math., 26(4) (2000), 359-368.

[14] Z. I. Szab o , Structure theorems on Riemannian spaces satisfying R(X,Y)R = 0 , The local version, J. Diff. Geom., 17 (1982), 531–582.

[15] A. Taleshian and N. Asghari, On LP-Sasakian Manifolds Satisfying Certain Conditions on the Concircular Curvature Tensor, Differ Geom-Dyn Syst., 12 (2010), 228-232.

[16] A. Taleshian and N. Asghari, On LP-Sasakian Manifolds, Bull. Math. Anal. Appl., 3 (2011), 45-51. International Journal of Mathematics Trends and Technology (IJMTT) – Volume 53 Number 1 January 2018 ISSN: 2231-5373 http://www.ijmttjournal.org Page 55.

[17] A. Taleshian and N. Asghari, On LP-Sasakian manifold satisfying certain conditions on the conharmonic curvature tensor, Studies in Nonlinear Sciences., 2(2) (2011), 50-53.

[18] A. Taleshian, D. G. Prakasha, K. vikas and N. Asghari, On the conharmonic curvature tensor of LP-Sasakian manifolds, Palestine J. Math., 3(1) (2014), 11-18.

[19] S. Tanno, Locally symmetric K-contact Riemannian manifold, Proc. Japan. Acad., 43 (1967), 581.

[20] K. Yano and M. Kon, Structure on Manifolds. Series in sMath. 3, World Scientific, Singapore, 1984.