IJPAM: Volume 70, No. 5 (2011)

LANDSBERG AND BERWALD SPACES OF DIMENSION TWO
WITH GENERALIZED $(\alpha, \beta)$-METRIC

T.N. Pandey$^1$, V.K. Chaubey$^2$, Sanjay K. Tripathi$^3$
$^{1,2}$Department of Mathematics and Statistics
D.D.U. Gorakhpur University
Gorakhpur, (U.P.), 273009, INDIA
$^3$Department of Mathematics
Almora Campus
Kumaun University
Almora, Uttaranchal, INDIA


Abstract. M. Matsumoto introduced the concept of $(\alpha, \beta)$ -Metric in the year, 1972. We have in 1999, the concept of generalized $(\alpha, \beta)$ -metric by taking $ \alpha, \beta^{1)},\beta^{2)}.....\beta^{m)} $ where $ \alpha=\sqrt{a_{ij}(x)y^{i}y^{j}} $ is a purely Riemannian metric and $ \beta^{1)},\beta^{2)}.....\beta^{m)} $ all are one form $ (\beta^{r)}=b^{r)}_{i}y^{i}) $. In the present paper, we had studied the condition under which a two-dimensional generalized $(\alpha, \beta)$ - Metric be a Landsberg and Berwald spaces in which the main scalar I plays an important role.

Received: February 6, 2011

AMS Subject Classification: 53B40, 53C60

Key Words and Phrases: Finsler space with $(\alpha, \beta)$-metric, Berwald space, Landsberg space

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 5