Toponogov comparison theorem for open triangles

Kei Kondo; Minoru Tanaka

doi:10.2748/tmj/1318338947

Toponogov comparison theorem for open triangles

Kei Kondo, Minoru Tanaka

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The aim of our article is to generalize the Toponogov comparison theorem to a complete Riemannian manifold with smooth convex boundary. A geodesic triangle will be replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a model surface will be replaced by the universal covering surface of a cylinder of revolution with totally geodesic boundary.

Original language	English
Pages (from-to)	363-396
Number of pages	34
Journal	Tohoku Mathematical Journal
Volume	63
Issue number	3
DOIs	https://doi.org/10.2748/tmj/1318338947
Publication status	Published - Sep 2011
Externally published	Yes

Keywords

Cut locus
Focal locus
Open triangle
Radial curvature
Riemannian manifold with boundary
Toponogov's comparison theorem

ASJC Scopus subject areas

Mathematics(all)

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10.2748/tmj/1318338947

Cite this

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title = "Toponogov comparison theorem for open triangles",

abstract = "The aim of our article is to generalize the Toponogov comparison theorem to a complete Riemannian manifold with smooth convex boundary. A geodesic triangle will be replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a model surface will be replaced by the universal covering surface of a cylinder of revolution with totally geodesic boundary.",

keywords = "Cut locus, Focal locus, Open triangle, Radial curvature, Riemannian manifold with boundary, Toponogov's comparison theorem",

author = "Kei Kondo and Minoru Tanaka",

year = "2011",

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doi = "10.2748/tmj/1318338947",

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AU - Kondo, Kei

AU - Tanaka, Minoru

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AB - The aim of our article is to generalize the Toponogov comparison theorem to a complete Riemannian manifold with smooth convex boundary. A geodesic triangle will be replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a model surface will be replaced by the universal covering surface of a cylinder of revolution with totally geodesic boundary.

KW - Cut locus

KW - Focal locus

KW - Open triangle

KW - Radial curvature

KW - Riemannian manifold with boundary

KW - Toponogov's comparison theorem

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SN - 0040-8735

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Toponogov comparison theorem for open triangles

Abstract

Keywords

ASJC Scopus subject areas

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