2001/09/10 by Zhongmin Shen, Shen, Zhongmin · 2 citations
Mathematics · #53C60 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:53C60
paper · pdf · doi:10.48550/arxiv.math/0109060
20 pages with three illustrations, latex file using texdraw.sty; Find related papers at http://www.math.iupui.edu/~zshen/index.html
arxiv created 2001/09/10 · arxiv updated 2009/11/30
In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero constant curvature. A recent example constructed by the author is projectively flat with zero curvature. In this paper, we introduce a technique to construct non-projectively flat Finsler metrics with zero curvature in each dimension. The technique can be used to construct many non-projectively flat Finsler metrics of constant curvature.