Finsler Metrics of Constant Positive Curvature on the Lie Group $s^3$
| dc.creator | Bao, David | |
| dc.creator | Shen, Zhongmin | |
| dc.date | 2000-11-12 | |
| dc.date.accessioned | 2026-07-07T04:38:32Z | |
| dc.date.available | 2026-07-07T04:38:32Z | |
| dc.description | 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 $S^3$. 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 $S^3$. 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. | |
| dc.description | 35 pages with a Maple program | |
| dc.identifier | https://arxiv.org/abs/math/0011071 | |
| dc.identifier | http://arxiv.org/abs/math/0011071 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60318 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 53C60 | |
| dc.title | Finsler Metrics of Constant Positive Curvature on the Lie Group $s^3$ | |
| dc.type | text |