CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

On a Class of Landsberg Metrics in Finsler Geometry

  Published:2009-12-01
 Printed: Dec 2009
  • Zhongmin Shen
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

In this paper, we study a long existing open problem on Landsberg metrics in Finsler geometry. We consider Finsler metrics defined by a Riemannian metric and a $1$-form on a manifold. We show that a \emph{regular} Finsler metric in this form is Landsbergian if and only if it is Berwaldian. We further show that there is a two-parameter family of functions, $\phi=\phi(s)$, for which there are a Riemannian metric $\alpha$ and a $1$-form $\beta$ on a manifold $M$ such that the scalar function $F=\alpha \phi (\beta/\alpha)$ on $TM$ is an almost regular Landsberg metric, but not a Berwald metric.
MSC Classifications: 53B40, 53C60 show english descriptions Finsler spaces and generalizations (areal metrics)
Finsler spaces and generalizations (areal metrics) [See also 58B20]
53B40 - Finsler spaces and generalizations (areal metrics)
53C60 - Finsler spaces and generalizations (areal metrics) [See also 58B20]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/