On Geodesic Equation and Main Scalar in Two Dimensional Finsler Space with Matsumoto Metrics

S. K. Narasimhamurthy, K. Chandru

Abstract


In this paper, we consider the two dimensional Finsler space with generalized Matsumoto metric and derived the geodesics equation in the Weierstrass form of differential equation. Then we find the main scalar for generalized Matsumoto metric in the two dimensional Finsler space.

Keywords


\((\alpha,\beta)\)-metrics; Geodesics; Two-dimensional Finsler space; Main scalar; Matsumoto metric

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References


P.L. Antonelli, R.S. Ingarden and M. Matsumto, The Theory of Sprays and Finsler Spaces with Application in Physics and Biology, Kluwer Acad. Publ., Dordrecht, Boston, London (1985).

V.K. Chaubey, B.N. Prasad and D.D. Tripathi, Equations of geodesic for a ((alpha,beta))-metric in a twodimensional Finsler space, J. Math. Comput. Sci. 3 (2013), 863 – 872.

M. Hasiguchi, S. Hojo and M. Matsumto, On landsberg spaces of two dimensions with ((alpha,beta))-metric, J. Korean. Math. Soc. 10 (1973), 17 – 26.

M. Kitayama, M. Azuma and M. Matsumoto, On Finsler space with ((alpha,beta))-metric, Regularity, Geodesics and main scalars, J. Hokkaido Univ. of Education 46 (1995), 1 – 10.

I.Y. Lee and H.S. Park, Finsler spaces with infinite series ((alpha,beta))-metric, J. Korean Math. Soc. 3 (2004), 567 – 589.

M. Matsumto, Geodesics of two dimensional Finsler spaces, Mathel. Comput. Modelling. 20 (1994), 1 – 23.

M. Matsumoto and H.S. Park, Equations of geodesic in two dimensional Finsler space with ((alpha,beta))-metric, Revue. Roumanie de pures et Appliques (1997), 787 – 793.

M. Matsumoto and H.S. Park, Equations of geodesic in teo dimensional Finsler space with ((alpha,beta))-metric, Tensors, N.S. 60 (1998), 89 – 93.

H.S. Park and I.Y. Lee, Equations of geodesic in a two dimensional Finsler space with a generalized Kropina metric, Bull. Korean Math. Soc. 37 (2000), N.S. 02, 337 – 346.




DOI: http://dx.doi.org/10.26713%2Fjims.v10i3.656

eISSN 0975-5748; pISSN 0974-875X