Projective Change between Two Finsler Spaces with (α, β)- metric

• Journal title : Kyungpook mathematical journal
• Volume 52, Issue 1,  2012, pp.81-89
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2012.52.1.81
Title & Authors
Projective Change between Two Finsler Spaces with (α, β)- metric
Kampalappa, Narasimhamurthy Senajji; Mylarappa, Vasantha Dogehalli;

Abstract
In the present paper, we nd the conditions to characterize projective change between two ($\small{{\alpha}}$, $\small{{\beta}}$)-metrics, such as Matsumoto metric $\small{L=\frac{{\alpha}^2}{{\alpha}-{\beta}}}$ and Randers metric $\small{\bar{L}=\bar{\alpha}+\bar{\beta}}$ on a manifold with dim $\small{n}$ > 2, where $\small{{\alpha}}$ and $\small{\bar{\alpha}}$ are two Riemannian metrics, $\small{{\beta}}$ and $\small{\bar{\beta}}$ are two non-zero 1-formas.
Keywords
Projective change;Matsumoto metric;Randers metric;Douglas metric;Locally Minkowski space;
Language
English
Cited by
References
1.
P. L. Antonelli, R. S. Ingarden and M. Matsumoto, The Theory of sprays and Finsler spaces with applications in Physics and Biology, Kluwer academic publishers, London, 1985.

2.
S. Bacso and M. Matsumoto, Projective change between Finsler spaces with ($\alpha$, $\beta$)- metric, Tensor N.S., 55(1994), 252-257.

3.
M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha press, Otsu, Saikawa, 1986.

4.
S. K. Narasimhamurthy and G. N. Latha Kumari, On a hypersurface of a special Finsler space with a metric L = ${\alpha}+{\beta}+\frac{\beta^{2}}{\alpha}$ , ADJM, 9(1)(2010), 36-44.

5.
Ningwei Cui and Yi-Bing Shen, Projective change between two classes of ($\alpha,\beta$)- metrics, Diff. Geom. and its Applications, 27(2009), 566-573.

6.
H. S. Park and Il-Yong Lee, On projectively at Finsler spaces with ($\alpha,\beta$)-metric, Comm. Korean Math. Soc., 14(2)(1999), 373-383.

7.
H. S. Park and Il-Yong Lee, The Randers changes of Finsler spaces with ($\alpha,\beta$)-metrics of Douglas type, J. Korean Math. Soc., 38(3)(2001), 503-521.

8.
H. S. Park and Y. Lee, Projective changes between a Finsler space with ($\alpha,\beta$)-metric and the associated Riemannian metric, Canad. J. Math., 60(2008), 443-456.

9.
Pradeep Kumar, S. K. Narasimhamurthy, H. G. Nagaraja and S. T. Aveesh, On a special hypersurface of a Finsler space with ($\alpha,\beta$)-metric, Tbilisi Mathematical Journal, 2(2009), 51-60.

10.
B. N. Prasad, B. N. Gupta and D. D. Singh, Conformal transformation in Finsler spaces with ($\alpha,\beta$)-metric, Indian J. Pure and Appl. Math., 18(4)(1961), 290-301.

11.
A. Rapsak, Uber die bahntreuen Abbildungen metrisher Raume, Publ. Math. Debrecen., 8(1961), 285-290.

12.
H. Rund, The differential geometry of Finsler spaces, Springer-Verlag, Berlin, 1959.

13.
Z. Shen, On Landsberg ($\alpha,\beta$)-metrics, 2006.

14.
Z. Shen and G. Civi Yildirim, On a class of projectively at metrics with constant flag curvature, Canad. J. Math., 60(2008), 443-456.

15.
C. Shibata, On Finsler spaces with an ($\alpha,\beta$)-metric, J. Hokkaido Univ. of Education, IIA, 35(1984), 1-6.

16.
H. Shimada and S. V. Sabau, Introduction to Matsumoto metric, Nonlinear Analysis, 63(2005), e165-e168.