Finsler Metrics of Constant Positive Curvature on the Lie Group S3

By David Bao, Zhongmin Shen. 2000

89 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/b0b952ff62924f7c9d8bf351dfe5aa95aa04347d

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In Astronomy and Astrophysics

Citations in the corpus

Zermelo navigation on Riemannian manifolds (2003, background): “The resulting Randers metric F has constant flag curvature K (see [8]).”
GEODESICS IN RANDERS SPACES OF CONSTANT CURVATURE (2005, background): “ly ﬁnitely many closed geodesics are rare. It should be noted that Randers metrics of constant curvature on the sphere have been studied from several distinct perspectives. These include the Bao–Shen [BS02] one-parameter family of examples developed from the Hopf ﬁbration on S3, and the approach of ”
Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry (2008, methodology): “Let us comment that the Finsler metric defined by (83) is equivalent to the family of Finsler metrics of constant, positive flag curvature on the Lie group S3, constructed in [7].”