ON PROJECTIVELY FLAT FINSLER SPACE WITH AN APPROXIMATE INFINITE SERIES (α,β)-METRIC

• Journal title : East Asian mathematical journal
• Volume 28, Issue 1,  2012, pp.25-36
• Publisher : Youngnam Mathematical Society
• DOI : 10.7858/eamj.2012.28.1.025
Title & Authors
ON PROJECTIVELY FLAT FINSLER SPACE WITH AN APPROXIMATE INFINITE SERIES (α,β)-METRIC
Lee, Il-Yong;

Abstract
We introduced a Finsler space $\small{F^n}$ with an approximate infinite series ($\small{{\alpha},{\beta}}$-metric $L({\alpha},{\beta}) Keywords Finsler space;projectively flat;in finite series ($\small{{\alpha},{\beta}}$)-metric;approximate in finite serie ($\small{{\alpha},{\beta}}$)-metric;homogeneous polynomials in ($\small{y^i}$) of degree r; Language English Cited by References 1. P. L. Antonelli, R. Ingarden and M. Matsumoto, The theory of sprays and Finsler spaces with applications in physics and biology, Kluwer QAcad. Publ., Netherlands, 1993. 2. T. Aikou, M. Hashiguchi and K. Yamauchi, On Matsumoto's Finsler space with time measure, Rep. Fac. Sci. Kagoshima Univ. (Math. Phys. Chem.) 23 (1990), 1-12. 3. S. Bacso and M. Matsumoto, Projective changes between Finsler spaces with (${\alpha},{\beta}$-metric, Tensor N. S. 55 (1994), 252-257. 4. M. Hashiguchi and Y. Ichijyo, Randers spaces with rectilinear geodesics, Rep. Fac. Sci. Kagoshima Univ. (Math. Phys. Chem.) 13 (1980), 33-40. 5. M. Matsumoto, Projective changes of Finsler metrics and projectively at Finsler spaces, Tensor N. S. 34 (1980), 303-315. 6. M. Matsumoto, A slope of a mountain is a Finsler surface with respect to time measure, J. Math. Kyoto Univ. 29 (1989), 17-25. 7. M. Matsumoto, Projectively flat Finsler spaces with (${\alpha},{\beta})-metric, Rep. on Math. Phys. 30 (1991), 15-20.

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