Funk Metrics and R-Flat Sprays
| dc.creator | Shen, Zhongmin | |
| dc.date | 2001-09-05 | |
| dc.date.accessioned | 2026-07-07T04:43:17Z | |
| dc.date.available | 2026-07-07T04:43:17Z | |
| dc.description | The well-known Funk metric F(x,y) is projectively flat with constant flag curvature K=-1/4 and the Hilbert metric H(x,y):=(F(x,y)+F(x,-y))/2 is projectively flat with constant curvature K=-1. These metrics are the special solutions to Hilbert's Fourth Problem. In this paper, we construct a non-trivial R-flat spray using the Funk metric. It is then an inverse problem in the calculus of variation to find a Finsler metric that induces the R-flat spray. We find an explicit solution to this inverse problem and obtain a non-trivial projectively flat Finsler metric with K=0. | |
| dc.description | Revised in June, 2001, 10 pages, other related papers can be downloaded from http://www.math.iupui.edu/~zshen/ | |
| dc.identifier | https://arxiv.org/abs/math/0109037 | |
| dc.identifier | http://arxiv.org/abs/math/0109037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62151 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 53B60 | |
| dc.title | Funk Metrics and R-Flat Sprays | |
| dc.type | text |