IJPAM: Volume 103, No. 2 (2015)

THE GENERALIZED $\beta-$CONFORMAL CHANGE OF
FINSLER METRIC

S.K. Tiwari$^1$, Anamika Rai$^2$
$^{1,2}$Department of Mathematics
K.S. Saket Post Graduate College
Ayodhya, Faizabad, 224 123, INDIA


Abstract. In the present paper, we have considered the generalized $\beta-$conformal change of Finsler metric $\ol L$ given by

\begin{displaymath}\ol L (x, y) = f(e^{\sigma (x)} L (x, y), {\beta ^{1)}},{\beta ^{2)}}, \ldots ,{\beta ^{m)}}),\end{displaymath}

where $f$ is any positively homogeneous function of degree one in $e^\sigma L$ and ${\beta ^{1)}}, {\beta ^{2)}},$ $\ldots ,{\beta ^{m)}}, {\beta ^{r)}} = b_i^{r)} (x)\,y^i$ and $\sigma (x)$ is a function of position only, known as conformal factor. The relation between the $v-$curvature tensor of the original Finsler space and Finsler space obtained by generalized $\beta-$conformal change has been obtained. Some basic properties of generalized $\beta-$conformal change of Finsler metric have been discussed and obtained useful results.

Received: April 17, 2015

AMS Subject Classification: 53B40, 53C60

Key Words and Phrases: generalized $\beta-$conformal change, generalized $\beta-$change, conformal change, $\beta-$change, Finsler metric

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DOI: 10.12732/ijpam.v103i2.11 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: 2015
Volume: 103
Issue: 2
Pages: 255 - 262


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