On Generalised Almost r-Contact Structure in a GF Manifold

Manisha M.  Kankarej; Jai Pratap Singh

doi:10.5269/bspm.70265

Manisha M. Kankarej Rochester Institute of Technology, Dubai.
Jai Pratap Singh B. S. N. V. P. G. College, Lucknow University, India.

Abstract

The main focus of this research is to study properties and theorems of a generalised almost r-contact structure in a GF manifold. GF structure endowed with a metric tensor, an affine connection, Nijenhuis tensor and $\pi$ plane field of a generalised almost r-contact structure are also a part of the study. Contact structures have applications in different branches of mathematics and physics which can be explored further with the help of examples presented in standard and generalized form in this research.

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References

Blair D., Kim J. S., and Tripathi M. M.: \emph{On the concircular curvature tensor of a contact metric manifold}, J. Korean Math. Soc., 42(5), \textbf{(2005)}, 883-892.
Boothby W. M. and Wang H. C.: \emph{On contact manifolds, Ann of Math}, (2), 721 - 734, \textbf{1958}.
Chandra V. and Lal S.: \emph{Almost Product Structure on Differentiable Manifolds with Nijenhuis Tensor}, International Jour. of Sci and Tech Research, Vol 8, \textbf{(2019)}, Issue 9.
Cho H.: \emph{Existence of almost contact structures on manifolds with G2-structures and generalisations}, Ph. D. Thesis, RIT, \textbf{2012}.
Debnath P.: \emph{Almost pseudo product structure, Differential Geometry and dynamical systems}, Vol 20, \textbf{(2018)}, 26-37.
Dube K. K. and Nivas R.: \emph{Almost r-contact hyperbolic structure in a product manifold}, Demonstratio Mathematica, Vol 11, No. 4, \textbf{(1978)}, pp 887 - 897.

Dube K. K.: \emph{On almost hyperbolic Hermite manifolds}, An. Univ. Din Timisoara, siri mat., vol. XI face 1, \textbf{(2004)}, pp 49 - 54.
Eum S. S.: \emph{Curvature tensors of 3-dimensional almost contact metric manifolds}, J. Korean Math. Soc.,21(2), \textbf{(1984)}, 249-255.
Geiges H.: \emph{Contact structures on (n-1) connected (2n+1) manifolds}, Pacific Jour. of Mathematics, Vol 161, No. 1, \textbf{(1993)}, 129-137.
Gupta V. C. and Dube R. : \emph{Almost r-contact structure in a product manifold}, Demonstratio Mathematica, Vol 14, No. 2, \textbf{(1981)}, pp 417 - 426.
Hit R.: \emph{On almost product manifolds}, Indian Journal of Pure and Applied Maths, Vol 4, No. 2, \textbf{(1973)}, pp 149-154.
Martinet J.: \emph{Formes de contact sur les varietes de dimension 3}, Springer lecture notes in math., Vol 209, \textbf{(1971)}, 142-163.
Mishra. R. S.: \emph{Almost contact manifolds with specified affine connexion}, Tensor (N. S.), Vol. 23, \textbf{(1992)}, pp 41-45.
Nivas R. and Suab A.: \emph{Half symmetric GF- connections}, Jour. Uni. of Kuwait, 16, \textbf{1989}.
Pandey S. B. and Dasila L.: \emph{On general differentiable manifold}, Uni. Sci. Phy. Sci., vol.7(2), \textbf{(1995)}, pp 147-152.
Sasaki S.: \emph{On the differentiable manifolds with certain structures which are closely related to the almost contact structure}, Tohoku Math Jour., Vol 2, (12) \textbf{(1960)}, pp 459 - 476.
Upadhyay M. D. and Dube K. K.: \emph{Almost contact hyperbolic $(f, g, \eta, \xi)$ - structure}, Acta Mathematica, Vol 28, No. 1-2, \textbf{(1976)}, pp 1-4.
Upadhyay M. D. and AgarwalA. K.: \emph{On a generalised r-contact structure in a complex manifold}, Demonstratio Mathematica, Vol 14, \textbf{(1981)}, No. 1.
Walker A. G.: \emph{On parallel field of partial null vector spaces}, Quart. Jour. Math , 22, \textbf{(1949)}, 135- -145.
Yano K.: \emph{Affine connexions in an almost product space}, Kodai Math Sem. Rep, \textbf{(1959)}, 11, 1-24.
Yano K. and Kon M.: \emph{Structures on Manifolds, Series in Pure Mathematics}, 3, World Scientific Publishing Co., Singapore, \textbf{1984}.