[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c180235

SOME RESULTS ON PROJECTIVE CURVATURE TENSOR IN SASAKIAN MANIFOLDS

Gautam, Umesh Kumar (Department of Mathematics and Astronomy University of Lucknow)
Haseeb, Abdul (Department of Mathematics Faculty of Science Jazan University)
Prasad, Rajendra (Department of Mathematics and Astronomy University of Lucknow)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.3, 2019 , pp. 881-896 More about this Journal

Abstract

In the present paper, we study certain curvature conditions satisfying by the projective curvature tensor in Sasakian manifolds with respect to the generalized-Tanaka-Webster connection. Finally, we give an example of a 3-dimensional Sasakian manifold with respect to the generalized-Tanaka-Webster connection.

Keywords

Sasakian manifolds; projective curvature tensor; g-Tanaka-Webster connection; ${\eta}$ -Einstein manifold;

Citations & Related Records

Reference

1	U. C. De, On $\phi$ -symmetric Kenmotsu manifolds, Int. Electron. J. Geom. 1 (2008), no. 1, 33-38.
2	U. C. De and G. Ghosh, On generalized Tanaka-Webster connection in Sasakian manifolds, Bull. Transilv. Univ. Brasov Ser. III 9(58) (2016), no. 2, 13-23.
3	M. K. Dwivedi and J.-S. Kim, On conharmonic curvature tensor in K-contact and Sasakian manifolds, Bull. Malays. Math. Sci. Soc. (2) 34 (2011), no. 1, 171-180.
4	I. Hasegawa and I. Mihai, Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata 102 (2003), 143-150. https://doi.org/10.1023/B:GEOM.0000006582.29685.22 DOI
5	V. A. Khan and M. A. Khan, Pseudo-slant submanifolds of a Sasakian manifold, Indian J. Pure Appl. Math. 38 (2007), no. 1, 31-42.
6	D. G. Prakasha, On $\phi$ -symmetric Kenmotsu manifolds with respect to quarter-symmetric metric connection, Int. Electron. J. Geom. 4 (2011), no. 1, 88-96.
7	S. Sasaki, Lecture note on almost contact manifolds. Part I, Tohoku University, 1965.
8	S. Sasaki, Lectures note on almost contact manifolds. Part II, Tohoku University, 1967.
9	S. Tachibana, On harmonic tensors in compact Sasakian spaces, Tohoku Math. J. (2) 17 (1965), 271-284. https://doi.org/10.2748/tmj/1178243549 DOI
10	S. S. Shukla and M. K. Shukla, On $\phi$ -symmetric para-Sasakian manifolds, Int. J. Math. Anal. (Ruse) 4 (2010), no. 13-16, 761-769.
11	T. Takahashi, Sasakian $\phi$ -symmetric spaces, Tohoku Math. J. (2) 29 (1977), no. 1, 91-113. https://doi.org/10.2748/tmj/1178240699 DOI
12	N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. (N.S.) 2 (1976), no. 1, 131-190. DOI
13	S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. (2) 21 (1969), 21-38. https://doi.org/10.2748/tmj/1178243031 DOI
14	S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), no. 1, 349-379. https://doi.org/10.2307/2001446 DOI
15	S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Dierential Geom. 13 (1978), no. 1, 25-41. http://projecteuclid.org/euclid.jdg/1214434345 DOI
16	C. P. Boyer and K. Galicki, Sasakian Geometry, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2008.
17	K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3, World Scientific Publishing Co., Singapore, 1984.
18	D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin, 1976.