On Landsberg general (α,β)-metrics with a conformal 1-form

2017/06/02 by Zhou, Shasha, Li, Benling
#53B40 #53C60 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.00533

Abstract

In this paper, we study almost regular Landsberg general (α,β)-metrics in Finsler geometry. The corresponding equivalent equations are given. By solving the equations, we give the classification of Landsberg general (α,β)-metrics under the conditon that β is closed and conformal to α. Under this condition, we prove that regular Landsberg general (α,β)-metrics must be Berwaldian when the dimension is greater than two. For the almost regular case, the classification also is given and some new non-Berwaldian Landsberg metrics are found.

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