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ISRN Geometry
Volume 2011 (2011), Article ID 505161, 16 pages
http://dx.doi.org/10.5402/2011/505161
Research Article

On Almost 𝝋 -Lagrange Spaces

Department of Mathematics, University of Allahabad, Allahabad 211 002, India

Received 12 October 2011; Accepted 13 November 2011

Academic Editors: A. Belhaj and M. Margenstern

Copyright © 2011 P. N. Pandey and Suresh K. Shukla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We initiate a study on the geometry of an almost 𝜑 -Lagrange space (APL-space in short). We obtain the expressions for the symmetric metric tensor, its inverse, semispray coefficients, solution curves of Euler-Lagrange equations, nonlinear connection, differential equation of autoparallel curves, coefficients of canonical metrical d-connection, and - and 𝑣 -deflection tensors in an APL-space. Corresponding expressions in a 𝜑 -Lagrange space and an almost Finsler Lagrange space (AFL-space in short) have also been deduced.