IJPAM: Volume 119, No. 4 (2018)

Title

MAIN SCALARS FOR A THREE DIMENSIONAL FINSLER
SPACE WITH A GENERAL $\left({\alpha ,\beta }\right)$-METRIC

Authors

Afsoon Goodarzian$^1$, Megerdich Toomanian$^2$,
and Mehdi Nadjafkhah$^3$
$^{1,2}$Department of Mathematics, Karaj Branch
Islamic Azad University
Karaj, I.R. IRAN
$^3$Department of Pure Mathematics
School of Mathematics
Iran University of Science and Technology, Narmak
Tehran, 16846-13114, I.R. IRAN

Abstract

In this paper, we find the main scalars of a three dimensional Finsler space equipped with a general $ \left(\alpha,\beta\right)$-metric $ F=\alpha+\kappa\beta+{{\varepsilon\beta}^{2}}/{\alpha} $ (where $ \kappa $ and $ \varepsilon $ are constants which are not zero simultaneously). Consequently, we will obtain results that give the main scalars of special three dimensional $ \left(\alpha,\beta\right)$-metrics such as square metric $ F=(\alpha+\beta )^2/\alpha $ and the first approximate matsumoto metric $ F=\alpha+\beta+{{\beta}^{2}}/{\alpha} $. Moreover, we present a sufficient and necessary condition for Finsler spaces equipped with $ \left(\alpha,\beta\right)$-metrics to be Riemannian spaces. Some fundamental theorems on main scalars of three dimensional Finsler spaces has also been dealt.

History

Received: March 13, 2018
Revised: August 3, 2018
Published: August 10, 2018

AMS Classification, Key Words

AMS Subject Classification: 58B20, 58J60
Key Words and Phrases: three dimensional Finsler space, $(\alpha,\beta)$-metric, Moor's frame, main scalar, the first matsumoto metric, square metric, Cartan tensor vector

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Bibliography

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A. Goodarzian, M. Nadjafikhah, M.Toomanian, On Main Scalar of Two Dimentional Finsler Spaces with $ \left(\alpha,\beta\right)$-Metrics, International Journal of Applied Mathematics $\&$ Statistics, 57, No. 3 (2018).

How to Cite?

DOI: 10.12732/ijpam.v119i4.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 119
Issue: 4
Pages: 661 - 683


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