Given the Finsler structure (M, F) on a manifold M, a Riemannian structure (M, h) and a linear connection on M are defined. They are obtained as the " average " of the Finsler structure and the Chern connection. This linear connection is the Levi-Civita connection of the Riemannian metric h. The relation between parallel transport of the Chern connection and the Levi-Civita connection of h are ...

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

The starting point of this work is the Bochner theorem on harmonics 1-forms stated at 1946. We show that many results on minimal foliations of codimension one and two on compact pseudo-Riemannian manifolds are at the origin of this theorem. We also prove the non existence of minimal Riemannian foliations of codimension one defined by a 1-form with finite global norm on complete non compact Riem...

An example is given of a plane topological torsion defect representing a cosmic wall double wall in teleparallel gravity.The parallel planar walls undergone a repulsive gravitational force due to Cartan torsion.This is the first example of a non-Riemannian double cosmic wall.It is shown that the walls oscillate with a speed that depends on torsion and on the surface density of the wall.Cartan t...

We define a novel metric on the space of closed planar curves which decomposes into three intuitive components. According to this metric centroid translations, scale changes and deformations are orthogonal, and the metric is also invariant with respect to reparameterizations of the curve. While earlier related Sobolev metrics for curves exhibit some general similarities to the novel metric prop...

We define a novel metric on the space of closed planar curves. According to this metric centroid translations, scale changes and deformations are orthogonal, and the metric is also invariant with respect to reparameterizations of the curve. The Riemannian structure that is induced on the space of curves is a smooth Riemannian manifold, which is isometric to a classical well-known manifold. As a...