The geometry on the slope of a mountain

TL;DR

This paper introduces the slope metric, a Finsler geometry on mountain slopes, exploring its existence, geodesic behavior, and comparing Finslerian and Riemannian areas on surfaces of revolution.

Contribution

It defines and analyzes the slope metric, a novel Finsler metric on mountain slopes, and compares its properties with classical Riemannian metrics.

Findings

Existence conditions for globally defined slope metrics.

Characterization of geodesic behavior on these surfaces.

Comparison results between Finslerian and Riemannian areas.

Abstract

The geometry on a slope of a mountain is the geometry of a Finsler metric, called here the {\it slope metric}. We study the existence of globally defined slope metrics on surfaces of revolution as well as the geodesic's behavior. A comparison between Finslerian and Riemannian areas of a bounded region is also studied.