We prove Hessian comparison theorems, Laplacian comparison theorems and volume comparison theorems of Finsler manifolds under various curvature conditions. As applications, we derive Mckean type theorems for the first eigenvalue of Finsler manifolds, as well as generalize a result on fundamental group due to Milnor to Finsler manifolds.

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

Abstract. The aim of this paper is to consider Busemann-type inequalities on Finsler manifolds. We actually formulate a rigidity conjecture: any Finsler manifold which is a Busemann NPC space is Berwaldian. This statement is supported by some theoretical results and numerical examples. The presented examples are obtained by using evolutionary techniques (genetic algorithms) which can be used fo...

we establish some relative volume comparison theorems for extremal volume forms of‎ ‎finsler manifolds under suitable curvature bounds‎. ‎as their applications‎, ‎we obtain some results on curvature and topology of finsler manifolds‎. ‎our results remove the usual assumption on s-curvature that is needed in the literature‎.

Let Fm = (M,F ) be a Finsler manifold and G be the Sasaki– Finsler metric on the slit tangent bundle TM0 = TM {0} of M . We express the scalar curvature ρ̃ of the Riemannian manifold (TM0, G) in terms of some geometrical objects of the Finsler manifold Fm. Then, we find necessary and sufficient conditions for ρ̃ to be a positively homogenenous function of degree zero with respect to the fiber coo...

In this paper, we prove that the Hodge-Laplace operator on strongly pseudoconvex compact complex Finsler manifolds is a self-adjoint elliptic operator. Then, from the decomposition theorem for self-adjoint elliptic operators, we obtain a Hodge decomposition theorem on strongly pseudoconvex compact complex Finsler manifolds. M.S.C. 2010: 53C56, 32Q99.

The aim of the present paper is to provide a global presentation, as complete as we can, of the theory of special Finsler manifolds. We introduce and investigate globally (or intrinsically, free from local coordinates) many of the most important and commonly used special Finsler manifolds : locally Minkowskian, Berwald, Landesberg, general Landesberg, P -reducible, C-reducible, semi-C-reducible...