CERTAIN RESULTS ON N(K)-CONTACT METRIC MANIFOLD

Main Article Content

GURUPADAVVA INGALAHALLI
S. C. ANIL
C. S. BAGEWADI

Abstract

In this paper, we study the curvature properties of N(k)-contact metric manifolds satisfying the conditions Projective Ricci pseudosymmetric Condition, W3-Ricci pseudosymmetric Condition, P.Q = 0, Q.P = 0, W3.Q = 0, Q.W3 = 0.

Keywords:
Contact Metric Manifolds, Projective curvature tensor, Ricci tensor, scalar curvature.

Article Details

How to Cite
INGALAHALLI, G., ANIL, S. C., & BAGEWADI, C. (2019). CERTAIN RESULTS ON N(K)-CONTACT METRIC MANIFOLD. Asian Journal of Mathematics and Computer Research, 26(3), 123-130. Retrieved from http://www.ikprress.org/index.php/AJOMCOR/article/view/4674
Section
Original Research Article

References

Tanno S. Ricci curvatures of contact Riemannian manifolds. Tohoku Math. J. 1988;40:441-448.

Blair DE, Koufogiorgos T, Papantoniou BJ. Contact metric manifolds satisfying a nullitycondition. Israel J. Math. 1995;91:189-214.

Shaikh AA, Baishya KK. On (k,μ)-contact metric manifolds. Differential Geometry-DynamicalSystems. 2006;8:253-261.

Baishya KK, Eyasmin S, Shaikh AA. On ϕ-recurrent generalized (k,μ)-contact metricmanifolds. Lobachevskii J. of Math. 2007;27:3-13.

De UC, Gazi AK. On ϕ-recurrent N(k)-contact metric manifolds. Math. J. Okayama Univ.2008;50:101-112.

Tripathi MM, Punam Gupta. (N(k), ξ)-semi-Riemannian manifolds:Semisymmetries.arXiv:1202.6138v [math.DG].

Ingalahalli et al.; AJOMCOR, 26(3): 123-130, 2019

Nagaraja HG, Somashekhara G. τ-curvature tensor in (k,μ)-contact manifolds. Proceedingsof the Estonian Academy of Sciences. 2012;61(1):20-28.

Gurupadavva Ingalahalli, Bagewadi CS. A Study on ϕ-Symmetric τ-curvature tensor in N(k)-contact metric manifold. Carpathian Math. Publ. 2014:6(2):203-211.

Majhi P, De UC. Classifications of n(k)-contact metric manifolds satisfying certain curvatureconditions. Acta Math. Univ. Comenianae. 2015;LXXXIV(1):167-178.

Deszcz R. On Ricci-pseudosymmetric warped products. Demonstratio Math. 1989;22:1053-1065.

Deszcz R. On pseudosymmetric spaces. Bull. Soc. Math. Belg. S´er. A. 1992;44(1):1-34.

Jahanara B, Haesen S, Sent¨urk Z, Verstraelen L. On the parallel transport of the Riccicurvatures. J. Geom. Phys. 2007;57:1771-1777.

Shaikh AA, Hui SK. On some classes of generalized quasi-Einstein manifolds. Commun. KoreanMath. Soc. 2009;24 (3):415-424.

Hui SK, Lemence RS. Ricci pseudosymmetric generalized quasi-Einstein manifolds. SUT J.Math. 2015;51:195-213.

Hui SK, Lemence RS, Chakraborty D. Ricci solitons on ricci pseudosymmetric (lcs)n-manifolds. arXiv: 1707.03618v1 [math.DG].

Blair DE. Contact manifolds in Riemannian geometry, lecture notes in mathematics. 509,Springer-Verlag. berlin-New-York; 1976.

De UC, Shaikh AA. Differential geometry of manifolds. Narosa Publishing House Pvt. Ltd.,New Delhi; 2007.

Pokhariyal GP. Curvature tensors and their relativistic significance III. Yokohama Math. J.1973;21:115-119.