Cyclic Pursuit on Compact Manifolds
Differential Geometry
2017-06-14 v5 Metric Geometry
Abstract
We study a form of cyclic pursuit on Riemannian manifolds with positive injectivity radius. We conjecture that on a compact manifold, the piecewise geodesic loop formed by connecting consecutive pursuit agents either collapses in finite time or converges to a closed geodesic. The main result is that this conjecture is valid for nonpositively curved compact manifolds.
Keywords
Cite
@article{arxiv.1602.03259,
title = {Cyclic Pursuit on Compact Manifolds},
author = {Dmitri Gekhtman},
journal= {arXiv preprint arXiv:1602.03259},
year = {2017}
}
Comments
Typos and minor details fixed