On Special Berwald Metrics

TL;DR

This paper investigates a class of Finsler metrics extending Berwald metrics, proving they are generalized Douglas-Weyl metrics, exploring isotropic flag curvature, and establishing the equivalence of Landsberg and weakly Landsberg curvatures within this class.

Contribution

It introduces a broader class of Finsler metrics containing Berwald metrics, proves they are generalized Douglas-Weyl, and links Landsberg and weakly Landsberg curvatures.

Findings

All metrics in this class are generalized Douglas-Weyl.

Isotropic flag curvature metrics are studied within this class.

Landsberg and weakly Landsberg curvatures are shown to be equivalent.

Abstract

In this paper, we study a class of Finsler metrics which contains the class of Berwald metrics as a special case. We prove that every Finsler metric in this class is a generalized Douglas-Weyl metric. Then we study isotropic flag curvature Finsler metrics in this class. Finally we show that on this class of Finsler metrics, the notion of Landsberg and weakly Landsberg curvature are equivalent.