IJPAM: Volume 80, No. 4 (2012)

ON GENERALIZED $C^{v}$-REDUCIBLE FINSLER SPACES

T.N. Pandey$^1$, V.K. Chaubey$^2$, Arunima Mishra$^3$
$^{1,2,3}$Department of Mathematics and Statistics
D.D.U. Gorakhpur University
Gorakhpur (U.P.), 273009, INDIA


Abstract. A Finsler space is said to be generalized $C^{v}$-Reducible Finsler Space whose $ C_{ijk}\vert _{h} $ can be written as product of tensor of type (0, 3) and (0, 1) such as,

$ LC_{ijk}\vert _{h}=A_{ijk}B_{h}+A_{ijh}B_{k}+A_{ihk}B_{j}+A_{hjk}B_{i}, \;\;\;\;\;\;\;\;\;\; A_{ijk}\neq \lambda C_{ijk} $
where, $ A_{i00}=0, \;\; A_{ij0}\neq 0 $ and $ B_{0}=0; \;\; A_{i00}=A_{ijk}y^{j}y^{k}, \;\; B_{0}=B_{i}y^{i} $.

In the present paper, we shall find out the value of $ A_{ijk} $, taking the value of $ B_{i} $ as $ m_{i} $ and $ n_{i} $, where $ m_{i} $ is $ C_{i}/C $ and $ n_{i} $ is unit vector perpendicular to the plane $ l_{i} $ and $ m_{i} $.

Received: April 4, 2012

AMS Subject Classification: 53B40, 53C60

Key Words and Phrases: two and three-dimensional Finsler spaces, main scalar, $C^{v}$-reducible Finsler 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: 2012
Volume: 80
Issue: 4