The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions

Symmetry Integrability and Geometry-Methods and Applications

article

Sorin V. Sabau¹ 

[1] School of Science, Department of Mathematics, Tokai University

关键词: Finsler manifolds;    ray;    co-ray (asymptotic ray);    cut locus;    co-points;    distance function;    Busemann function;   

DOI  :  10.3842/SIGMA.2016.036

来源: National Academy of Science of Ukraine

【 摘 要 】

We show that the co-rays to a ray in a complete non-compact Finsler manifold contain geodesic segments to upper level sets of Busemann functions. Moreover, we characterise the co-point set to a ray as the cut locus of such level sets. The structure theorem of the co-point set on a surface, namely that is a local tree, and other properties follow immediately from the known results about the cut locus. We point out that some of our findings, in special the relation of co-point set to the upper lever sets, are new even for Riemannian manifolds.

【 授权许可】

Unknown