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.

In this note we study extra large spherical conemanifolds in dimension 2 (though many of our resultsz and techniques extend to higher dimensions. A 2-dimensional spherical cone manifold is a metric space where all but finitely many points has a neighborhood isometric to a neighborhood of a point on the round sphere S. The exceptional points (cone points) have neighboroods isometric to a spheric...

We define an L2-disparity measure between curved high-order meshes and parameterized manifolds in terms of an L2 norm. The main application of the proposed definition is to measure and improve the distance between a curved high-order mesh and a target parameterized curve or surface. The approach allows considering meshes with the nodes on top of the curve or surface (interpolative), or floating...

There are very few known examples of manifolds with positive sectional curvature. Apart from the compact rank one symmetric spaces, they exist only in dimensions 24 and below and are all obtained as quotients of a compact Lie group equipped with a biinvariant metric under an isometric group action. They consist of certain homogeneous spaces in dimensions 6, 7, 12, 13 and 24 due to Berger [Be], ...