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Finsler Metrics of Constant Positive Curvature on the Lie Group S 3
Author(s) -
Bao David,
Shen Z.
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003344
Subject(s) - hopf fibration , mathematics , lie group , constant (computer programming) , curvature , invariant (physics) , killing vector field , metric (unit) , pure mathematics , finsler manifold , constant curvature , field (mathematics) , mathematical analysis , mathematical physics , geometry , ricci curvature , computer science , programming language , operations management , economics
Guided by the Hopf fibration, a family (indexed by a positive constant K ) of right invariant Riemannian metrics on the Lie group S 3 is singled out. Using the Yasuda–Shimada paper as an inspiration, a privileged right invariant Killing field of constant length is determined for each K > 1. Each such Riemannian metric couples with the corresponding Killing field to produce a y ‐global and explicit Randers metric on S 3 . Employing the machinery of spray curvature and Berwald's formula, it is proved directly that the said Randers metric has constant positive flag curvature K , as predicted by Yasuda–Shimada. It is explained why this family of Finslerian space forms is not projectively flat.