2000/11/12 by David Bao, Zhongmin Shen, Bao, David +1 · 1 citation
Mathematics · Physics and Astronomy · #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:53C60
paper · pdf · doi:10.48550/arxiv.math/0011071
35 pages with a Maple program
arxiv created 2000/11/12 · openalex publication_date 2000/11/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Guided by the Hopf fibration, we single out a family (indexed by a positive constant K) of right invariant Riemannian metrics on the Lie group S3. Using the Yasuda-Shimada theorem as an inspiration, we determine for each K>1 a privileged right invariant Killing field of constant length. Each such Riemannian metric pairs with the corresponding Killing field to produce a y-global and \it explicit Randers metric on S3. Using the machinery of spray curvature and Berwald's formula for it, we prove directly that the said Randers metric has constant positive flag curvature K, as predicted by the Yasuda-Shimada theorem. We also explain why this family of Finslerian space forms is NOT projectively flat.