IJPAM: Volume 78, No. 6 (2012)

THE $\mathcal{L}$-DUAL OF
A GENERALIZED MATSUMOTO SPACE

Gauree Shanker$^1$, Ravindra Yadav$^2$
$^{1,2}$Department of Mathematics and Statistics
Banasthali University
Banasthali, Rajasthan, 304022, INDIA


Abstract. One of the most well studied Finsler metrics are the $(\alpha,
\beta)$-metrics. Among them, Randers, Kropina and Matsumoto metrics are well known brand names in modern Finsler geometry. Recently a lot of work has been done on the generalized m- Kropina and generalized Matsumoto metrics.

In [#!DH96!#,#!DH97!#,#!IMSH08!#] the $\mathcal{L}$-dual of Randers, Kropina and Matsumoto space were introduced. Recently, in [#!GS11!#], the $\mathcal{L}$-dual of a generalized m-Kropina space has been introduced. In this paper we study the $\mathcal{L}$-dual of a generalized Matsumoto space.

Received: January 1, 2012

AMS Subject Classification: 53B40, 53C60

Key Words and Phrases: Finsler space, Cartan space, generalized Matsumoto space, the duality between Finsler and Cartan spaces, Legendre transformation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 6