DOI QR코드

DOI QR Code

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)
  • Received : 2018.05.28
  • Accepted : 2018.07.19
  • Published : 2019.07.31

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

References

  1. D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin, 1976.
  2. C. P. Boyer and K. Galicki, Sasakian Geometry, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2008.
  3. U. C. De, On $\phi$-symmetric Kenmotsu manifolds, Int. Electron. J. Geom. 1 (2008), no. 1, 33-38.
  4. 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.
  5. 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.
  6. 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
  7. 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.
  8. 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.
  9. S. Sasaki, Lecture note on almost contact manifolds. Part I, Tohoku University, 1965.
  10. S. Sasaki, Lectures note on almost contact manifolds. Part II, Tohoku University, 1967.
  11. 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.
  12. S. Tachibana, On harmonic tensors in compact Sasakian spaces, Tohoku Math. J. (2) 17 (1965), 271-284. https://doi.org/10.2748/tmj/1178243549
  13. T. Takahashi, Sasakian $\phi$-symmetric spaces, Tohoku Math. J. (2) 29 (1977), no. 1, 91-113. https://doi.org/10.2748/tmj/1178240699
  14. N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. (N.S.) 2 (1976), no. 1, 131-190. https://doi.org/10.4099/math1924.2.131
  15. 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
  16. S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), no. 1, 349-379. https://doi.org/10.2307/2001446
  17. 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 https://doi.org/10.4310/jdg/1214434345
  18. K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3, World Scientific Publishing Co., Singapore, 1984.