On Zermelo'-like problems: a Gauss-Bonnet inequality and a E. Hopf theorem

Details On Zermelo'-like problems: a Gauss-Bonnet inequality and a E. Hopf theorem On Zermelo'-like problems: a Gauss-Bonnet inequality and a E. Hopf theorem

2007-06-10

arxiv.org/abs/0706.1366v1

Mathematics

Optimization and Control

27 pages, 1 figure

Scientific paper

The goal of this paper is to describe Zermelo's navigation problem on Riemannian manifolds as a time-optimal control problem and give an efficient method in order to evaluate its control curvature. We will show that up to change the Riemannian metric on the manifold the control curvature of Zermelo's problem has a simple to handle expression which naturally leads to a generalization of the classical Gauss-Bonnet formula in an inequality. This Gauss-Bonnet inequality enables to generalize for Zermelo's problems the E. Hopf theorem on flatness of Riemannian tori without conjugate points.

Affiliated with

Also associated with

No associations

Rating

On Zermelo'-like problems: a Gauss-Bonnet inequality and a E. Hopf theorem 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 On Zermelo'-like problems: a Gauss-Bonnet inequality and a E. Hopf theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Zermelo'-like problems: a Gauss-Bonnet inequality and a E. Hopf theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-677856