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Year 2019, Volume: 7 Issue: 2, 312 - 318, 15.10.2019

Abstract

References

  • [1] Blair, , D. E., Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics.509, Springer-Verlag, Berlin-New York, 1976.
  • [2] Blair, D. E., Riemannian Geometry of Contact and Sympletic Manifolds, Progress in Math-ematics. 203, Birkhauser Boston, Inc., Boston, MA, 2001.
  • [3] Calvaruso, G., and Perrone, D., Contact pseudo-metric manifolds, Di erential Geom. Appl.,28(2010), 615-634.
  • [4] Calvaruso, G., and Perrone, D., H-contact semi-Riemannian manifolds, J. Geom. Phys.71(2013),11-21.
  • [5] Derdzinski, A., and Roter, W., Some theorems on conformally symmetric manifolds, Tensor(N.S.)32(1978),11-23.
  • [6] Derdzinski, A., and Roter, W., On conformally symmetric manifolds with metrics of indices0 and 1, Tensor (N.S.) 31(1977), 255-259.
  • [7] Perrone, D., Curvature of K-contact semi-Riemannian manifolds, Can. Math. Bull57(2014),401-412.
  • [8] Perrone, D., Contact pseudo-metric manifolds of constant curvature and CR geometry,Results. Math. 66(2014), 213-225.
  • [9] Tanno, S., Locally symmetric K-conatct Riemannian manifolds, Proc. Japan Acad.43(1967),581-543.
  • [10] Takahasi, T., Sasakian manifold with pseudo-Riemannian metrics, Tohoku Math. J.21(1969),271-290.
  • [11] Yildiz, A., and Ata, E., On a type of K-contact manifolds, Hacettepe J. Math. and Stat.41(2012),567-571.
  • [12] Zhen, G., Cabrerizo, J. l., Fenandez, L. M., and Fenandez, M., On -conformally at K-contact metric manifolds, Indian J. Pure Appl. Math, 28(1997), 725-734.
  • [13] Zhen, G., The conformally symmetric K-contact manifolds, Chinese Quarterly Journal ofMath., 7(1992),5-10.

Classifications of $K$-Contact Semi-Riemannian Manifolds

Year 2019, Volume: 7 Issue: 2, 312 - 318, 15.10.2019

Abstract

The object of the present paper is to characterize a K-contact semi-Riemannian manifold satisfying certain curvature conditions. We study Ricci semi-symmetric K-contact semi-Riemannian manifolds and obtain an equivalent condition. Next we prove that a K-contact semi-Riemannian manifold is of harmonic conformal curvature tensor if and only if the manifold is an Einstein manifold. Also we study $\xi$-conformally flat K-contact semi-Riemannian manifolds. Finally, we charecterize conformally semisymmetric Lorentzian $K$-contact manifolds.


References

  • [1] Blair, , D. E., Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics.509, Springer-Verlag, Berlin-New York, 1976.
  • [2] Blair, D. E., Riemannian Geometry of Contact and Sympletic Manifolds, Progress in Math-ematics. 203, Birkhauser Boston, Inc., Boston, MA, 2001.
  • [3] Calvaruso, G., and Perrone, D., Contact pseudo-metric manifolds, Di erential Geom. Appl.,28(2010), 615-634.
  • [4] Calvaruso, G., and Perrone, D., H-contact semi-Riemannian manifolds, J. Geom. Phys.71(2013),11-21.
  • [5] Derdzinski, A., and Roter, W., Some theorems on conformally symmetric manifolds, Tensor(N.S.)32(1978),11-23.
  • [6] Derdzinski, A., and Roter, W., On conformally symmetric manifolds with metrics of indices0 and 1, Tensor (N.S.) 31(1977), 255-259.
  • [7] Perrone, D., Curvature of K-contact semi-Riemannian manifolds, Can. Math. Bull57(2014),401-412.
  • [8] Perrone, D., Contact pseudo-metric manifolds of constant curvature and CR geometry,Results. Math. 66(2014), 213-225.
  • [9] Tanno, S., Locally symmetric K-conatct Riemannian manifolds, Proc. Japan Acad.43(1967),581-543.
  • [10] Takahasi, T., Sasakian manifold with pseudo-Riemannian metrics, Tohoku Math. J.21(1969),271-290.
  • [11] Yildiz, A., and Ata, E., On a type of K-contact manifolds, Hacettepe J. Math. and Stat.41(2012),567-571.
  • [12] Zhen, G., Cabrerizo, J. l., Fenandez, L. M., and Fenandez, M., On -conformally at K-contact metric manifolds, Indian J. Pure Appl. Math, 28(1997), 725-734.
  • [13] Zhen, G., The conformally symmetric K-contact manifolds, Chinese Quarterly Journal ofMath., 7(1992),5-10.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Chiranjib Dey 0000-0002-6453-6707

Uday Chand De 0000-0002-8990-4609

Publication Date October 15, 2019
Submission Date December 2, 2018
Acceptance Date August 1, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Dey, C., & De, U. C. (2019). Classifications of $K$-Contact Semi-Riemannian Manifolds. Konuralp Journal of Mathematics, 7(2), 312-318.
AMA Dey C, De UC. Classifications of $K$-Contact Semi-Riemannian Manifolds. Konuralp J. Math. October 2019;7(2):312-318.
Chicago Dey, Chiranjib, and Uday Chand De. “Classifications of $K$-Contact Semi-Riemannian Manifolds”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 312-18.
EndNote Dey C, De UC (October 1, 2019) Classifications of $K$-Contact Semi-Riemannian Manifolds. Konuralp Journal of Mathematics 7 2 312–318.
IEEE C. Dey and U. C. De, “Classifications of $K$-Contact Semi-Riemannian Manifolds”, Konuralp J. Math., vol. 7, no. 2, pp. 312–318, 2019.
ISNAD Dey, Chiranjib - De, Uday Chand. “Classifications of $K$-Contact Semi-Riemannian Manifolds”. Konuralp Journal of Mathematics 7/2 (October 2019), 312-318.
JAMA Dey C, De UC. Classifications of $K$-Contact Semi-Riemannian Manifolds. Konuralp J. Math. 2019;7:312–318.
MLA Dey, Chiranjib and Uday Chand De. “Classifications of $K$-Contact Semi-Riemannian Manifolds”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 312-8.
Vancouver Dey C, De UC. Classifications of $K$-Contact Semi-Riemannian Manifolds. Konuralp J. Math. 2019;7(2):312-8.
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