Curvature approximation of 3D manifolds in 4D space

On curvature homogeneous 4D Lorentzian manifolds

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH3 for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, CH2 manifolds that are not homogeneous. PACS numbers: 04.20, 02.40 AMS classification scheme numbers: 53C50

On Stretch curvature of Finsler manifolds

In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every  (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...

Local Projections Method and Curvature Approximation of 3D Polygonal Models

Mesh processing is a wide area which consists of several approaches, heavily specific for each task. We present a novel approach to mesh processing using the Local Projections method. The described method makes benefit of wide variety of image processing algorithms, very similar to 3D tasks, and implements a conversion mechanism to make possible use of these processes on polygonal models. We al...

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form