A Gauss-Bonnet Type Formula on Riemann-Finsler surfaces with non-constant indicatrix volume

TL;DR

This paper establishes a Gauss-Bonnet type formula for Riemann-Finsler surfaces with variable indicatrix volume and explores properties of N-parallels on Landsberg surfaces, extending classical differential geometry results.

Contribution

It introduces a Gauss-Bonnet type formula for a new class of Riemann-Finsler surfaces with non-constant indicatrix volume and analyzes N-parallels on Landsberg surfaces.

Findings

Proved a Gauss-Bonnet type formula for these surfaces.

Derived a Hadamard type theorem for N-parallels.

Extended classical geometry results to Finsler surfaces with variable indicatrix volume.

Abstract

We prove a Gauss-Bonnet type formula for Riemann-Finsler surfaces of non-constant indicatrix volume and with regular piecewise smooth boundary. We give a Hadamard type theorem for N-parallels of a Landsberg surface.