On a generalized Finsler warped product metrics with vanishing Landsberg curvature

TL;DR

This paper investigates a class of Finsler metrics, deriving explicit curvature formulas and characterizing generalized warped product metrics with vanishing Landsberg curvature, including examples of non-regular Landsberg metrics.

Contribution

It provides explicit curvature expressions and PDE characterizations for generalized Finsler warped product metrics with vanishing Landsberg curvature, including novel non-regular examples.

Findings

Derived explicit formulas for Berwald and Landsberg curvatures.

Established PDE systems characterizing generalized warped product metrics.

Constructed examples of non-regular Landsberg metrics not of Berwald type.

Abstract

In this paper, we study weakly orthogonally invariant Finsler metrics and derive explicit expressions for their Berwald and Landsberg curvatures. We then obtain the system of partial differential equations characterizing generalized Finsler warped product metrics on $I \times \mathbb{R}^n$, which form a subclass of weakly orthogonally invariant Finsler metrics, under the conditions of vanishing Berwald and Landsberg curvatures. As an application, we construct examples of non-regular Landsberg metrics that are not of Berwald type.