HYPERSURFACES OF A FINSLER SPACE WITH DEFORMED BERWALD-INFINITE SERIES METRIC

Abstract

The rationale of this paper is to study the Finslerian hypersurfaces of a Finsler space with the special deformed Berwald-Infinite series metric. Further examined under which condition, the Finslerian hypersurfaces of this special metric becomes a hyperplane of first, second and third kinds

Keywords

• Finslerian hypersurface,Infinite series metric and Berwald metric

References

1. Berwald, L., (1929), ¨U ber die n-dimensionalen Geometrien konstanter Kr¨ummung, in denen die Ger- aden die k¨urzesten sind. Math. Z. 30, pp. 449-469.
2. Chaubey, V. K. and Mishra, A., (2017), Hypersurface of a Finsler Space with Special (α, β)-metric, Journal of Contemporary Mathematical Analysis, 52, pp. 1-7.
3. Chaubey, V. K. and Tripathi, B. K., (2014), Finslerian Hypersurface of a Finsler Spaces with Special (γ, β)-metric, Journal of Dynamical System and Geometric Theories, 12(1), pp. 19-27.
4. Kitayama, M., (2002), On Finslerian hypersurfaces given by β− change, Balkan Journal of Geometry and Its Applications, 7-2, pp. 49-55.
5. Lee, I. Y., Park, H. Y. and Lee, Y. D., (2001), On a hypersurface of a special Finsler spaces with a metric (α +βα), Korean J. Math. Sciences, 8, pp. 93-101. 2
6. Lee, I Y and Park, H. S., (2004), Finsler spaces with infinite series (α, β)-metric, J.Korean Math. Society,41(3), pp. 567-589.
7. Matsumoto, M., (1985), The induced and intrinsic Finsler connections of a hypersurface and Finslerian projective geometry, J. Math. Kyoto Univ., 25, pp.107-144.
8. Pandey, T. N. and Tripathi B. K., (2007), On a hypersurface of a Finsler Space with Special (α, β)- Metric, Tensor, N. S., 68, pp. 158-166.

9. Singh, U. P. and Kumari, Bindu, (2001), On a hypersurface of a Matsumoto space, Indian J. pure appl. Math., 32, pp. 521-531.
10. Shen, Z. M. and Yu, C. T., (2014), On Einstein square metrics, Publ. Math. Debr., 85, (3–4), pp. 413-424.