We study an important class of Finsler metrics — Randers metrics. We classify Randers metrics of scalar flag curvature whose S-curvatures are isotropic. This class of Randers metrics contains all projectively flat Randers metrics with isotropic S-curvature and Randers metrics of constant flag curvature.

Scoliosis is the abnormal lateral curvature and rotation of the spine. In the past this deformity has been linked with moral depravity, as in the case of Richard III. Treatment for scoliosis began with Hippocrates's use of boards and axial distortion. Today, bracing and surgery are used either to correct the deformity or to prevent further progression. In the past, however, exercise regimens ha...

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric i...

In this paper we study the two-dimensional complex Finsler spaces with (α, β)-metrics by using the complex Berwald frame. A special approach is dedicated to the complex Berwald spaces with (α, β) metrics. We establish the necessary and sufficient condition so that the complex Randers and Kropina spaces should be complex Berwald spaces, and we will illustrate the existence of these spaces in som...

In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G3. Also, we classify linear Weingarten rotational surfaces in G3. A linear Weingarten surface is the surface having a linear equation between the Gaussian curvature and the mean curvature of a surface. In last section, we construct isotropic rotational surfaces in G3 with prescribed mean curvature...

We prove that if (M, g) is a compact locally irreducible Riemannian manifold with nonnegative isotropic curvature, then one of the following possibilities hold: (i) M admits a metric with positive isotropic curvature (ii) (M, g) is isometric to a locally symmetric space (iii) (M, g) is Kähler and biholomorphic to CP n. This is implied by the following two results: (i) Let (M, g) be a compact, l...

By unicorns, I am referring to those mythical single-horned horse-like creatures for which there are only rumoured sightings by a privileged few. A similar situation exists in Finsler differential geometry. There, one has the hierarchy Euclidean ⊂ Minkowskian & Riemannian ⊂ Berwald ⊂ Landsberg among five families of metrics, in which the first two inclusions are known to be proper by virtue of ...

dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.