Mean Curvature of the Indicatrix of Finsler Manifold

TL;DR

This paper derives an expression for the mean curvature of the indicatrix in Finsler manifolds using the fundamental function, linking geometric properties to the defining metrics.

Contribution

It provides a new formula for the mean curvature of the indicatrix in Finsler geometry based on the fundamental function.

Findings

Mean curvature expressed in terms of the fundamental function

Link between Finsler metric and indicatrix geometry

Enhanced understanding of Finsler manifold curvature properties

Abstract

Fundamental function in Finsler manifold defines a metrices that depend on a point and a direction. At any point tangent space is a Riemannian and an indicatrix is a convex hypersurface. In this paper a mean curvature of the indicatrix is expressed in terms of fundamental function.