A Gauss-Bonnet-type formula on Riemann-Finsler surfaces with nonconstant indicatrix volume

Abstract

We prove a Gauss-Bonnet-type formula for Riemann-Finsler surfaces of nonconstant indicatrix volume and with regular piecewise $C^{\infty }$-boundary. We give a Hadamard-type theorem for $N$-parallels of a Landsberg surface.