PROJECTIVELY FLAT FINSLER SPACE WITH AN APPROXIMATE MATSUMOTO METRIC

Title & Authors
PROJECTIVELY FLAT FINSLER SPACE WITH AN APPROXIMATE MATSUMOTO METRIC
Park, Hong-Suh; Lee, Il-Yong; Park, Ha-Yong; Kim, Byung-Doo;

Abstract
The Matsumoto metric is an ($\small{\alpha,\;\bata}$)-metric which is an exact formulation of the model of Finsler space. Lately, this metric was expressed as an infinite series form for $$\small{\mid}$\beat$\small{\mid}$\;<\;$\small{\mid}$\alpha$\small{\mid}$$ by the first author. He introduced an approximate Matsumoto metric as the ($\small{\alpha,\;\bata}$)-metric of finite series form and investigated it in [11]. The purpose of the present paper is devoted to finding the condition for a Finsler space with an approximate Matsumoto metric to be projectively flat.
Keywords
Finsler space;projectively flat;Matsumoto metric;approximate Matsumoto metric;homogeneous polynomials in ($\small{y^{i}}$) of degree r;
Language
English
Cited by
1.
ON THE SECOND APPROXIMATE MATSUMOTO METRIC,;;;

대한수학회보, 2014. vol.51. 1, pp.115-128
1.
ON THE SECOND APPROXIMATE MATSUMOTO METRIC, Bulletin of the Korean Mathematical Society, 2014, 51, 1, 115
References
1.
The theory of sprays and Finsler spaces with applications in physics and biology, 1993.

2.
Rep. Fac. Sci. Kagoshima Univ.(Math. Phys. Chem.), 1990. vol.23. pp.1-12

3.
Rep. Fac. Sci. Kagoshima Univ.(Math. Phys. Chem.), 1980. vol.13. pp.33-40

4.
Tensor, N.S., 1980. vol.34. pp.303-315

5.
J. Math. Kyoto Univ., 1989. vol.29. pp.17-25

6.
Rep. on Math. Phys., 1991. vol.30. pp.15-20

7.
Tensor, N. S., 1998. vol.60. pp.123-134

8.
Foundations of Finsler geometry and special Finsler spaces, 1986.

9.
Tensor, N. S., 1995. vol.56. pp.142-148

10.
Commun. Korean Math. Soc., 1999. vol.14. 2, pp.373-383

11.
Indian J. pure and appl. Math., 2002. vol.34. 1, pp.59-77