To prove Theorems 1, we need to obtain a Laplacian comparison theorem on the Finsler manifold and then follow the method of Schoen and Yau in [7] (see also [9]).

Shen, "A universal volume comparison theorem for Finsler manifolds and related results," Canadian Journal of Mathematics, vol.

The pair (M, F) is called

Finsler manifold. In particular, if g does not depend on y, we recover the Riemannian geometry.

Mathematicians at the University of Malaga in Spain examine the subtleties of both the Cauch boundary for a generalized and possible non-symmetric distance, and the Gromov compactification for any, possibly incomplete,

Finsler manifold. They also introduce the new Busemann compactification, relating it to the previous two completions, and give a full description of the causal boundary of any standard conformally stationary spacetime.

We say that the triple [F.sup.m] = (M, M' F) with satisfying ([F.sub.1]) and ([F.sup.2]) is a Finsler manifold and F is the fundamental function of [F.sup.m].

Let [F.sup.3] = (M, M, F) be a 3-dimensional Finsler manifold and C be a smooth curve in Ml given locally by the parametric Equations;

It is said to be a Finsler manifold if the length s of any curve t [right arrow] ([x.sup.1](t), ..., [x.sup.m](t)) (a [less than or equal to] t [less than or equal to] b) is given by an integral

A Finsler manifold M has a tangent bundle [pi]: TM [right arrow] M.

They cover differentiable manifolds, Finsler metrics, connections and curvatures, S-curvature, Riemann curvature, projective changes, comparison theorems, fundamental groups of

Finsler manifolds, minimal immersions and harmonic maps, Einstein metrics, and miscellaneous topics.

Fueki: On

Finsler manifolds with the Chern-Rund connection whose projectivised tangent bundle has the Sasaki type metric, Nonlinear Anal., Real World Appl., 10(2009), 191-202.

Contributors address such topics as two curvature-driven problems in Riemann-Finsler geometry, curvature properties of certain metrics, a connectiveness principle in positively curved

Finsler manifolds, Riemann-Finsler surfaces, Finsler geometry in the tangent bundle, and topics in Finsler-inspired differential geometry such as perturbations of constant connection Wagner spaces, path geometries of almost-Grassmann structures, Ehresmann connections in relation to metrics and good metric derivatives and dynamical systems of the Lagrangian and Hamiltonian mechanical systems.

Bektas: Helices of the 3-dimensional

Finsler manifolds, J.