Finsler Metrics of Constant Positive Curvature on the Lie Group S3 |
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Authors: | Bao David; Shen Z |
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Institution: | Department of Mathematics, University of Houston Houston, TX 77204-3008, USA, bao{at}math.uh.edu
Department of Mathematical Sciences, IUPUI Indianapolis, IN 46202-3216, USA, zshen{at}math.iupui.edu |
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Abstract: | Guided by the Hopf fibration, a family (indexed by a positiveconstant K) of right invariant Riemannian metrics on the Liegroup S3 is singled out. Using the YasudaShimada paperas an inspiration, a privileged right invariant Killing fieldof constant length is determined for each K > 1. Each suchRiemannian metric couples with the corresponding Killing fieldto produce a y-global and explicit Randers metric on S3. Employingthe machinery of spray curvature and Berwald's formula, it isproved directly that the said Randers metric has constant positiveflag curvature K, as predicted by YasudaShimada. It isexplained why this family of Finslerian space forms is not projectivelyflat. |
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