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 ...

Abstract In this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these by warped product. Using the obtained equations, manufacture new product vanishing These contain metric introduced Berwald and spherically symmetric given Mo-Zhu.

In this paper, we establish a closer relation between the Berwald scalar curvature and [Formula: see text]-curvature. fact, prove that Finsler metric has isotropic if only it weakly For metrics of flag text]-curvature, they have almost text]-curvature is isotropic.

We define a manifold M where objects c ∈ M are curves, which we parameterize as c : S → lR (n ≥ 2, S is the circle). We study geometries on the manifold of curves, provided by Sobolev–type Riemannian metrics H . These metrics have been shown to regularize gradient flows used in Computer Vision applications, see [13, 16] and references therein. We provide some basic results of H metrics; and, fo...

We study a relation between certain extensions of the Clifford bundle and Finsler type structures that naturally generalize standard (pseudo)-Riemannian metric Dirac matrices. show for flat metrics there is triangle map constructed from [Formula: see text]-forms on text], extension relevant operators.

The study of moduli space and Teichmüller space has a long history. These two spaces lie in the intersections of the researches in many areas of mathematics and physics. Many deep results have been obtained in history by many famous mathematicians. Here we will only mention a few that are closely related to our discussions. Riemann was the first who considered the space M of all complex structu...