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On cylindrical symmetric Finsler metrics with vanishing Douglas curvature

Newton Solórzano, Dik Lujerio, Víctor León, Alexis Rodríguez

Abstract

In this paper, we consider the cylindrically symmetric Finsler metrics and we obtain their Douglas curvature. Furthermore, we obtain the differential equation system of the cylindrically symmetric Finsler metrics with vanishing Douglas curvature. Many examples are included.

On cylindrical symmetric Finsler metrics with vanishing Douglas curvature

Abstract

In this paper, we consider the cylindrically symmetric Finsler metrics and we obtain their Douglas curvature. Furthermore, we obtain the differential equation system of the cylindrically symmetric Finsler metrics with vanishing Douglas curvature. Many examples are included.

Paper Structure

This paper contains 4 sections, 6 theorems, 81 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Douglas curvature
  4. Douglas metric examples

Key Result

Proposition 1

Let $F=\vert\overline{y}\vert{\phi(x^0,r,s,z)}$ be a Finsler metric defined on $M$, where $z=\frac{y^0}{\vert\overline{y}\vert},$$r=\vert\overline{x}\vert$, $s=\frac{\langle\overline{x},\overline{y}\rangle}{\vert\overline{y}\vert}$ and $TM$ with coordinates coordx-coordy. Then $F$ is a Finsler metri

Theorems & Definitions (17)

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