Finslerian Hypersurfaces and Generalized β-Change of Finsler Metric

S. K. Tiwari; Anamika Rai

doi:10.6180/jase.2016.19.2.01

Finslerian Hypersurfaces and Generalized β-Change of Finsler Metric

S. K. Tiwari This email address is being protected from spambots. You need JavaScript enabled to view it.¹ and Anamika Rai¹

¹Department of Mathematics, K. S. Saket Post Graduate College, Ayodhya, Faizabad 224123, India

Received: May 4, 2015
Accepted: October 22, 2015
Publication Date: June 1, 2016

Download Citation: ||https://doi.org/10.6180/jase.2016.19.2.01

ABSTRACT

In the present paper, using the field of linear frame [1-3], we shall considered Finslerian hypersurfaces given by generalized β-change of Finsler metric. The generalized change of Finsler metric is given by L = f (L, β¹⁾, β²⁾,…, β^m)), where f is any positively homogeneous function of degree one in L and β¹⁾, β²⁾,…, β^m). Our purpose is to give some relations between the original Finslerian hypersurface and the other which is Finslerian given by generalized β-change. We have shown that generalizedchange makes three types of hypersurfaces invariant under certain conditions. Also, we have obtained the conditions under which this change will be a hyperplane of first, second and third kind.

Keywords: Finslerian Hypersurfaces, Generalized change, Finsler Metric, Hyperplane

REFERENCES

[1] Kikuchi, S., “On the Theory of Subspace,” Tensor, N. S., Vol. 2, pp. 6769 (1952).
[2] Kitayama, M., “Finslerian Hypersurfaces and Metric Transformation,” Tensor, N. S., Vol. 60, pp. 171178 (1998).
[3] Moor, A., “Finsler Raume Von Identischer Torsion,” Acta Sci. Math.,Vol. 34, pp. 279288 (1973).
[4] Matsumoto, M., “On Transformations of Locally Minkowskian Space,” Tensor, N. S., Vol. 22, pp. 103111 (1971).
[5] Shibata, C., “On Invariant Tensors of Beta-change of Finsler Metrices,” J. Math. Kyoto Univ., Vol. 24, pp. 163188 (1984).
[6] Pandey, T. N., Srivastava, E. and Tiwari, B., “On Generalized (, ) Metric,” Proceeding of Third Conference of Int. Acad. of Phy. Sci., pp. 311323 (1999).
[7] Pandey, S. B., Chaubey, V. K. and Tripathi, Sanjay K., “Berwald Connection and Geodesic of a Finsler Space with Generalized (, ) Metric,” J. Rajasthan Acad. Phy. Sci., Vol. 8, No. 1, pp. 3948 (2009).
[8] Pandey,T.N.,Prasad, B.N.andChaubey,V.K.,“Main Scalar of Two Dimensional Finsler Spaces with Generalized (, ) Metric,” Bull. Pure App. Math., Vol. 4, No. 2, pp. 168177 (2010).
[9] Pandey, T. N., Chaubey, V. K. and Tripathi, Sanjay, K., Landsberg and Berwald Spaces of Mathematics, Vol. 70, No. 5, pp. 691699 (2011).
[10] Matsumoto, M., “The Induced and Intrinsic Connections of a Hypersurface and Finslerian Projective Geometry,” J. Math. Kyoto Univ., Vol. 25, pp. 107144 (1985).
[11] Rapsak, A., “Eine Neue Charkterisierung Finslersher Rume Skalarer und Konstanter Krmmung und Projektiv-ebene Rume,” Acta Math. Acad. Sci. Hunger, Vol.8,No.1,pp.118(1857).doi:10.1007/BF02025229
[12] Haimovici, M., “Varietes Totalement Exremales Et Varieties Totalement Geodesiques Dons Les Expaces de Finsler,”Ann.Sci.,Univ.Jassy,Vol.25,pp.559644(1939).