The Journal of the Indian Mathematical Society

Bankteshwar Tiwari ¹

Affiliations
1 DST-CIMS, Faculty of Science, Banaras Hindu University Varanasi, 221 005, IN

Abstract

The purpose of the present paper is to study hypersurfaces of a Special semi-C-reducible Finsler space. It is found that, if the torsion vector of enveloping space Fⁿ is tangential to its hypersurface Hⁿ⁻¹ and n > 3, then the hypersurface is also a Special semi-C-reducible Finsler space. Finally surfaces in a three dimensional Special semi-C-reducible Finsler space have been studied. The notations and terminologies are referred to the monograph [8].

Keywords

Finsler Space, Hypersurface of a Finsler Space, Semi-C-Reducible Finsler Space.

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Bankteshwar Tiwari ¹, Manoj Kumar ¹

Affiliations
1 DST-Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi-221 005, IN

Abstract

In the present paper a special (α, β)-metric, which is considered as a generalization of the Rander's metric as well as of the Z. Shen's square metric, has been studied and the conditions for a Finsler space with this special metric to be a Berwald space, a Douglas space and Weakly-Berwald space respectively, have also been found.

Keywords

Finsler Space, (α, β)-Metric, Berwald Spaces, Douglas Spaces, Weakly Berwald Spaces.

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Bankteshwar Tiwari ¹

Affiliations
1 Department of Mathematics, B.R.D.P.G. College, Deoria, (U.P.) 274001, IN

Abstract

The purpose of the present paper is to study the geometrical properties of a generalized Lagrange space L_n with metric L_gij (x,y) = g_ij (x,y)+(1/c²)y_iy_j and to find the relations among metric tensors, angular metric tensors, Cartan tensors of generalized Lagrange space L_n, corresponding Lagrange space L*_n, generalized Finsler space F_n and associated Finsler space F*_n, where g_ij (x,y) be metric tensor of a generalized Finsler space and y_i = g_ij (x,y)y^j. Moreover the concept of C-reducibility has been introduced in Lagrange and generalized Lagrange spaces.

Keywords

Finsler Space, Lagrange Space, Generalized Lagrange Space.

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