In this note, we show that the examples of non-Berwaldian Landsberg surfaces with vanishing flag curvature, obtained in [5] , are fact Berwaldian. Consequently, Bryant's claim is still unverified.

Systolic complexes were introduced in Januszkiewicz–Świa̧tkowski [12] and, independently, in Haglund [10]. They are simply connected simplicial complexes satisfying a certain condition that we call simplicial nonpositive curvature (abbreviated SNPC). The condition is local and purely combinatorial. It neither implies nor is implied by nonpositive curvature for geodesic metrics on complexes, but ...

In this paper, we study the well-known unicorn problem for Finsler metrics. First, prove that every homogeneous Landsberg surface has isotropic flag curvature. Then by using particular form of curvature, a rigidity result on surfaces. Indeed, is Riemannian or locally Minkowskian. Thus, give an affirmative answer to Xu-Deng's conjecture in two-dimensional manifolds.

There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves $I$-invariant projective vector fields. The sub-algebra $C$-projective fields, leaving $H$-curvature invariant, has been studied extensively. Here on a closed Finsler space with negative definite Ricci curvature reduces to that Killing Moreover, if an admits such...

Building upon earlier work of T. Brady, we construct locally CAT(0) classifying spaces for those Artin groups which are three dimensional and which satisfy the FC (flag complex) condition. The approach is to verify the “link condition” by applying gluing arguments for CAT(1) spaces and by using the curvature testing techniques of M. Elder and J. McCammond.

In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n ≥ 3. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat.