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The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions
Інший ID:
2010 Mathematics Subject Classification: 53C60; 53C22
DOI:10.3842/SIGMA.2016.036
DOI:10.3842/SIGMA.2016.036
Посилання:
The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions / S.V. Sabau // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 12 назв. — англ.
Підтримка:
I am grateful to Professor M. Tanaka for bringing this topic into my attention and for many
illuminating discussions. I am also deeply indebted to the anonymous referees for their constructive
criticism and extremely useful suggestions that improved the manuscript enormously.
Also I thank to N. Boonnam for reading an early version of the paper.
Дата:
2016
Переглядів:
580
Завантажень:
250
Анотація:
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.
