Finsler Metrics of Constant Positive Curvature on the Lie Group <i>S</i> ³

Guided by the Hopf fibration, a family (indexed by a positive constant K) of right invariant Riemannian metrics on the Lie group S3 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 S3. 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.