The cut loci on Ellipsoids and certain Liouville manifolds

Jin Ichi Itoh; Kazuyoshi Kiyohara

doi:10.4310/AJM.2010.v14.n2.a6

The cut loci on Ellipsoids and certain Liouville manifolds

Jin Ichi Itoh, Kazuyoshi Kiyohara

Graduate School of Natural Science and Technology

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

7 Citations (Scopus)

Abstract

We show that some riemannian manifolds diffeomorphic to the sphere have the property that the cut loci of general points are smoothly embedded closed disks of codimension one. Ellipsoids with distinct axes are typical examples of such manifolds.

Original language	English
Pages (from-to)	257-290
Number of pages	34
Journal	Asian Journal of Mathematics
Volume	14
Issue number	2
DOIs	https://doi.org/10.4310/AJM.2010.v14.n2.a6
Publication status	Published - Jun 2010

Keywords

Cut locus
Ellipsoid
Integrable geodesic flow
Liouville manifold

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.4310/AJM.2010.v14.n2.a6

Cite this

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title = "The cut loci on Ellipsoids and certain Liouville manifolds",

abstract = "We show that some riemannian manifolds diffeomorphic to the sphere have the property that the cut loci of general points are smoothly embedded closed disks of codimension one. Ellipsoids with distinct axes are typical examples of such manifolds.",

keywords = "Cut locus, Ellipsoid, Integrable geodesic flow, Liouville manifold",

author = "Itoh, {Jin Ichi} and Kazuyoshi Kiyohara",

year = "2010",

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doi = "10.4310/AJM.2010.v14.n2.a6",

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AU - Kiyohara, Kazuyoshi

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AB - We show that some riemannian manifolds diffeomorphic to the sphere have the property that the cut loci of general points are smoothly embedded closed disks of codimension one. Ellipsoids with distinct axes are typical examples of such manifolds.

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KW - Ellipsoid

KW - Integrable geodesic flow

KW - Liouville manifold

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JO - Asian Journal of Mathematics

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The cut loci on Ellipsoids and certain Liouville manifolds

Abstract

Keywords

ASJC Scopus subject areas

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