Some results of Kenmotsu manifolds admitting Schouten-Van Kampen connection

Authors

  • Gurupadavva Ingalahalli Department of Mathematics, J.N.N. College of Engineering, Navule, Shimoga - 577204, Karnataka, INDIA.
  • S.C. Anil Department of Mathematics, J.N.N. College of Engineering, Navule, Shimoga - 577204, Karnataka, INDIA
  • C.S. Bagewadi Department of Mathematics, Kuvempu University, Shankaraghatta - 577 451, Shimoga, Karnataka, INDIA.

Keywords:

Ricci tensor, Curvature tensor, Kenmotsu Manifolds

Abstract

In this paper we study some curvature properties of Kenmotsu manifolds with respect to Schouten-Van Kampen connection satisfying Pseudo-Projectively flat, ξ-Pseudo-Projectively flat, φ-Pseudo-Projectively Semi-symmetric, Pseudo-Pseudo-Projectively flat, W*8-flat, ξ-W*8-flat, φ-W*8-semi symmetric, Pseudo-W*8-flat conditions.

Downloads

Download data is not yet available.

References

K.K. Baishya and P.R. Chowdhury, Kenmotsu Manifold with some Curvature Conditions, Annales Univ. Sci. Budapest., 59, (2016), 55-65.

A. Bejancu and H.R. Farran, Foliations and geometric structures, Springer Science and Business Media, 580 (2006).

D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, 509, Springer-Verlag, berlin-New-York, 1976.

S.K. Chaubey and R.H. Ojha, On the m-projective curvature tensor of a Kenmotsu manifold, Differential Geometry-Dynamical Systems, 12, (2010), 52-60.

U.C. De and A.A. Shaikh, Differential Geometry of Manifolds, Narosa Publishing House Pvt. Ltd., New Delhi, 2007.

U.C. De, On ϕ-symmetric Kenmotsu manifolds, International electronic Jour. of geometry, 1, (2008), 33-38.

G. Ghosh, On Schouten-van Kampen Connection in Sasakian Manifolds, Bol. Soc. Paran. Mat. . 36 (4), (2018), 171-182.

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

Gurupadavva Ingalahalli and C.S. Bagewadi, A study on Conservative C-Bochner curvature tensor in K-contact and Kenmotsu manifolds admitting semi-symmetric metric connection, ISRN Geometry, (2012), 1-14.

S.K. Hui and D. Chakraborty, Infinitesimal CL-transformations on Kenmotsu manifolds, Bangmod Int. J. Math and Comp. Sci., 3, (2017), 1-9.

S. Ianus, Some almost product strucutres on Manifolds with linear connection, Kodai Math. Sem. Rep., 23, (1971), 305-310.

K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., 24, (1972), 93-103.

D.L. Kiran Kumar, H.G. Nagaraja and S.H. Naveen Kumar, Some curvature properties of Kenmotsu Manifolds with Schouten-Van Kampen Connection, Bulletin of the Transilvania University of Brasov, 12 (2), (2019), 351-364.

[H.G. Nagaraja and D.L. Kiran Kumar, Kenmotsu Manifolds Admitting Schouten-Van Kampen Connection, Facta Universitatis (NIS) Ser. Math. Inform., 34, (2019), 23-34.

Z. Olszak, The Schouten-van Kampen affine connection adapted to an almost fparag contact metric structure, Publications de l'Institute Mathematique, 94, (2013), 31-42.

C. Ozgur, On weakly symmetric Kenmotsu manifolds, Differential Geometry-Dynamical Systems, 8, (2006), 204-209.

D.G. Prakasha and B.S. Hadimani, On the conharmonic curvature tensor of Kenmotsu manifolds with generalized Tanaka-Webster connection, Misolc. Math. Notes, 19, (2018), 491-503.

G.P. Pokhariyal, Relativistic significance of curvature tensors, International Journal of Mathematics and Mathematical Sciences, 5 (1), (1982), 133-139.

J.A. Scouten and Van Kampen, Zur Einbettungs-und Krmmungs theorie nichtholonomer Gebilde, Mathematische Annalen, 103, (1930), 752-783.

A.A. Shaikh and S.K. Hui, On Locally ϕ-Symmetric β-Kenmotsu Manifolds, Extracta Mathematicae, 24 (3), (2009), 301-316.

M.M. Tripathi and Punam Gupta, τ-curvature tensor on a semi-Riemannian manifold, J. Adv. Math. Stud., 4 (1), (2011), 117-129.

M.M. Tripathi and Punam Gupta, (N(k),ξ )-semi-Riemannian manifolds: Semisymmetries, arXiv:1202.6138v [math.DG] 28(Feb 2012).

A. Yildiz, f-Kenmotsu manifolds with the Schouten-van Kampen connection, Publi. Inst. Math. 102, (2017), 93-105.

Downloads

Published

2020-12-31

How to Cite

Ingalahalli, G., Anil, S. ., & Bagewadi, . C. . (2020). Some results of Kenmotsu manifolds admitting Schouten-Van Kampen connection. MathLAB Journal, 7, 191-199. Retrieved from https://purkh.com/index.php/mathlab/article/view/959

Issue

Section

Research Articles