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On a generalized Finsler warped product metrics with vanishing Landsberg curvature

Newton Solórzano, Dik D. Lujerio Garcia, Víctor León, Alexis Rodríguez Carranza

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.

On a generalized Finsler warped product metrics with vanishing Landsberg curvature

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 , 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.

Paper Structure

This paper contains 5 sections, 10 theorems, 128 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Berwald and Landsberg curvatures
  4. On a generalized Finsler warped product metrics whit vanishing Lansberg curvature
  5. Non Belwardian pseudo Finsler metric with vanishing Landsberg curvature

Key Result

Theorem 1

Let $F=\vert\overline{y}\vert{\phi(x^0,r,z)}$ be a Finsler metric defined on $M=I\times \mathbb{B}^n(\rho)\subset \mathbb{R}\times\mathbb{R}^n,$ where $z=\frac{y^0}{\vert\overline{y}\vert},$$r=\vert\overline{x}\vert$ and $TM$ with coordinates coordx-coordy. Then $F$ is Landsberg metric if and only i

Theorems & Definitions (17)

  • Theorem 1
  • Proposition 1
  • Proposition 2
  • Corollary 1
  • Theorem 2
  • proof
  • Lemma 1
  • proof
  • Theorem 3
  • proof
  • ...and 7 more