On general (α, β)-metrics of weak Landsberg type

2017/06/13 by Ala, A., Behzadi, A., Rafiei-Rad, M.
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1706.03973

Abstract

In this paper, we study general (α,β)-metrics which α is a Riemannian metric and β is an one-form. We have proven that every weak Landsberg general (α,β)-metric is a Berwald metric, where β is a closed and conformal one-form. This show that there exist no generalized unicorn metric in this class of general (α,β)-metric. Further, We show that F is a Landsberg general (α,β)-metric if and only if it is weak Landsberg general (α,β)-metric, where β is a closed and conformal one-form.

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