International Journal of Mathematics Trends and Technology
Volume 46 | Number 4 | Year 2017 | Article Id. IJMTT-V46P538 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P538
Dr. Shankar Lal, "Cartesian Product of Hyperbolic (F,g,r,η,έ) Structure," International Journal of Mathematics Trends and Technology (IJMTT), vol. 46, no. 4, pp. 264-271, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V46P538
In the present paper we have studied the Cartesian product of hyperbolic (F,g,r,η,έ) structure. Cartesian product of two manifolds has been defined and studied by Pandey. In this paper we have taken Cartesian product of (F,g,r,η,έ) structure manifolds, where r is some finite integer and studied some properties of curvature and Ricci tensor of such a product manifold. In section one; introductory part of hyperbolic (F,g,r,η,έ) structure is defined. In section two, we prove that the some theorems of product of hyperbolic (F,g,r,η,έ) structure as well as others important structure. In section three, we have studied some properties of Curvature and Ricci tensor and some theorems. In the end we have discussed the Cartesian product of hyperbolic (F,g,r,η,έ) structure.
1. Adati, T. and T. Miyazawa, (1979): On P-Sasakian manifolds satisfying certain condition, Tensor, (N.S), vol. 33 pp. 173-178.
2. Bagewadi, C.S. and Venkatesha, (2006): Torseforming vector field in a 3-dimensional trans- Sasakian manifold Differential Geometry- Dynamical Systems, vol. 8 pp.23-28.
3. De, U.C. and A. Sarkar, (2009). On a type of P-Sasakian manifold. Math. Reports, vol. 11 (61) pp.139-144.
4. De, U.C. and A.A. Shaikh, (2007). Differential Geometry of Manifolds. Alpha Science International Ltd. Oxford, UK, pp: 259-272.
5. Dube, K.K. (1973): On almost hyperbolic Hermite manifolds, An. Univ. Din Timisoara, siri mat. Vol. XI, face I pp. 49-54.
6. Hicks, N.J. (1965): Notes on Differential Geometry, D. Van Nastrand company inc., New York.
7. Pandey, H.B. (1981): Cartesian product of two manifolds, Indian Journal of Pure & Applied Mathematics Vol. 12, No. 1, pp 55-60.
8. Pant, J. (1986): Hypersurface immersed in a GF-structure manifold, Demonstratio Mathematica, Warszawa Poland,Vol. XIX No. 3, pp 693-697.
9. Upreti, J. (1999): Manifold with generalized r-contact product structure, J. of T.S.I. vol. 17 pp. 82-88.
10. Yano, K. and Kon, M. (1984): Structures on manifolds, word scientific publishing co. pvt. Ltd. Singapore.
PDF 
Citation 
Abstract 
Keywords 
References