Related papers: Finsler Metrics with Bounded Cartan Torsions
We study orthonormal normal sections of two-dimensional immersions in $\mathbb R^{n+2},$ $n\ge 2$, at which these sections are critical for a functional of total torsion. In particular, we establish upper bounds for the torsion coefficients…
We discuss the generalized Newton-Cartan geometries that can serve as gravitational background fields for particles and strings. In order to enable us to define affine connections that are invariant under all the symmetries of the structure…
In the present paper, we introduce and investigate various types of harmonic Finsler manifolds and find out the interrelation between them. We give some characterizations of such spaces in terms of the mean curvature of geodesic spheres and…
We study metric spaces with bounded rough angles. E. Le Donne, T. Rajala and E. Walsberg implicitly used this notion to show that infinite snowflakes can not be isometrically embedded into finite dimensional Banach spaces. We show that…
In our previous work, we introduced a special type of Hermitian metrics called {\em torsion-critical,} which are non-K\"ahler critical points of the $L^2$-norm of Chern torsion over the space of all Hermitian metrics with unit volume on a…
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $W=\int H^2$ under compactly supported infinitesimal conformal variations. Examples include all constant mean…
We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are K\"ahler with torsion. It is shown that such a geometry inherits similar…
We prove that the Ricci scalar curvature and the Berwald scalar curvature of a two-dimensional Finsler space, considered over a vector field on the 3-dimensional flat space, are naturally related to 2-dimensional electro-capillary phenomena…
We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.
In this paper, we study the integral curvatures of Finsler manifolds and prove several Myers type theorems.
This paper introduces a novel theoretical framework for identifying Lagrangian Coherent Structures (LCS) in manifolds with non-constant curvature, extending the theory to Finsler manifolds. By leveraging Riemannian and Finsler geometry, we…
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We associate a geometrically determined moving frame field to such a surface and using the…
We study the set of curvature functions which a given compact manifold with boundary can possess. First, we prove that the sign demanded by the Gauss-Bonnet Theorem is a necessary and sufficient condition for a given function to be the…
On a manifold with boundary, we deform the metric conformally. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in…
This article starts with the mathematical definition, concrete description, and physical meaning of Cartan's torsion. I proceed with the argumentation that torsion is required for the description of intrinsic spin. Moreover I argue that the…
In this paper, we introduce an asymmetric metric on the space of marked Euclidean triangles, and we prove several properties of this metric, including two equivalent definitions of this metric, one of them comparing ratios of functions of…
We obtain bounds on the least dimension of an affine space that can contain an $n$-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points. This problem is closely related to the generalized…
In this paper, we give the geometric meaning of hypersurfaces with constant mean curvature in a Finsler manifold by using volume preserving variation. Then we give the correspondence between principal curvatures of submanifolds by a…
In this paper, we study systematically the concentration properties of Finsler metric measure manifolds. We establish the relationships between the concentration properties and the observable diameter, isoperimetric inequalities and the…
Given a Finslerian metric $F$ on a $C^4$-manifold, conformal deformations of $F$ preserving the $R$-Einstein criterion are presented. In particular, locally conformal invariance between two Finslerian $R$-Einstein metrics is characterized.