We provide a proof that nonholonomically constrained Ricci flows of (pseudo) Riemannian metrics positively result into nonsymmetric metrics (as explicit examples, we consider flows of some physically valuable exact solutions in general relativity). There are constructed and analyzed three classes of solutions of Ricci flow evolution equations defining nonholonomic deformations of Taub NUT, Schw...

Based on the previous research, in this paper we study the dual flatness of a special class of Finsler metrics called general (α, β)-metrics, which is defined by a Riemannian metric α and a 1-form β. By using a new kind of deformation technique, we construct many non-trivial explicit dually flat general (α, β)-metrics.

This paper is a continuation of a series of papers, dealing with contact sub-Riemannian metrics onR3. We study the special case of contact metrics that correspond to isoperimetric problems on the plane. The purpose is to understand the nature of the corresponding optimal synthesis, at least locally. It is equivalent to studying the associated sub-Riemannian spheres of small radius. It appears t...

In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical properties. We propose numerical solutions for the initial and boundary value...

To motivate the construction, let us begin by looking at the much simpler situation that arises in real dimension 2. First of all, we all know that a complex curve (or Riemann surface) is the same thing as an oriented 2manifoldM equipped with a conformal class [g] of Riemannian (i.e. positivedefinite) metrics. If g is any Riemannian metric on M , and if u : M → R is any smooth positive function...

Though graph cut based segmentation is a widely-used technique, it is known that segmentation of a thin, elongated structure is challenging due to the "shrinking problem". On the other hand, many segmentation targets in medical image analysis have such thin structures. Therefore, the conventional graph cut method is not suitable to be applied to them. In this study, we developed a graph cut seg...

We investigate Kaluza-Klein metrics with a recurrent lightlike vector field over a pseudo-Riemannian manifold (B, g).