Mathematics – Differential Geometry
Scientific paper
2001-09-05
Mathematics
Differential Geometry
Revised in June, 2001, 10 pages, other related papers can be downloaded from http://www.math.iupui.edu/~zshen/
Scientific paper
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.
No associations
LandOfFree
Funk Metrics and R-Flat Sprays does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Funk Metrics and R-Flat Sprays, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Funk Metrics and R-Flat Sprays will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-715238