A note on L. Zhou's result on Finsler surfaces with $K = 0$ and $J = 0$

TL;DR

This paper clarifies that certain Finsler surfaces previously thought to be non-Berwaldian with zero flag curvature are actually Berwaldian, challenging Bryant's claim and refining the understanding of such surfaces.

Contribution

It demonstrates that examples of non-Berwaldian Landsberg surfaces with zero flag curvature are actually Berwaldian, correcting prior assumptions and leaving Bryant's claim unverified.

Findings

Examples are actually Berwaldian surfaces.

Bryant's claim remains unverified.

Refinement of classification of Finsler surfaces.

Abstract

In this note, we show that the examples of non Berwaldian Landsberg surfaces with vanishing flag curvature, obtained in \cite{Zhou}, are in fact Berwaldian. Consequently, Bryant's claim is still unverified.