IJPAM: Volume 107, No. 4 (2016)

NONHOLONOMIC FRAMES FOR A FINSLER SPACE
WITH GENERAL $(\alpha, \beta)$-METRIC

Gauree Shanker$^1$, Sruthy Asha Baby$^2$
$^1$Centre for Mathematics and Statistics
Central University of Punjab
Bathinda, Punjab, 151001, INDIA
$^2$Department of Mathematics and Statistics
Banasthali University
Banasthali, Rajasthan, 304022, INDIA


Abstract. The main purpose of this paper is to first determine the two Finsler deformations of the special $(\alpha, \beta)$-metric $F = \alpha +\epsilon \beta + k \frac{\beta^2}{\alpha }$, where $\epsilon$ and $k$ are constants. Consequently, we obtain the nonholonomic frame for Finsler space with special $(\alpha, \beta)$-metric which is often considered as the generalization of Randers metric as well as Z. Shen's square metric. Further, we obtain some results which give nonholonomic frame for Finsler spaces with certain $(\alpha, \beta)$–metrics such as Randers metric, a special $(\alpha, \beta)$-metric $\alpha + \frac{\beta^2}{\alpha}$, first approximate Matsumoto metric and Finsler space with square metric.

Received: February 27, 2016

AMS Subject Classification: 53B40, 53C60

Key Words and Phrases: Finsler space with $(\alpha, \beta)$-metric, generalized lagrange metric, nonholonomic Finsler frame

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DOI: 10.12732/ijpam.v107i4.19 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 4
Pages: 1013 - 1023


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