On Almost φ-Lagrange Spaces

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 h- 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.