The Cut Locus of Riemannian Manifolds: a Surface of Revolution

Abstract

Abstract

This article reviews the structure theorems of the cut locus for very familiar surfaces of revolution. Some properties of the cut locus of a point of a Riemannian manifold are also discussed.

Keywords: Riemannian manifolds, surface of revolution, homeomorphic

^*Corresponding author:

E-mail: tanaka@tokai-u.jp

How to Cite

Citation Format

Tanaka*, M. . (2018). The Cut Locus of Riemannian Manifolds: a Surface of Revolution. CURRENT APPLIED SCIENCE AND TECHNOLOGY, 34-40.

References

Myers, S. B., 1935. Connections between differential geometry and topology. I. Simply connected surfaces, Duke Mathematics Journal, 1, 376-391.
Myers, S. B., 1936. Connections between differential geometry and topology. II. Closed surfaces, Duke Mathematics Journal, 2(1), 95-102.
Gluck, H. and Singer, D., 1979. Scattering of geodesic fields. II, Ann.Math.110, 205-225.
Hebda, J., 1994. Metric structure of cut loci in surfaces and Ambrose’s problem, Journal of Differential Geometry, 40, 621-642.
Hartman, P., 1964. Geodesic parallel coordinates in the large, Amer. J. math. 86, 705-727.

Author Information

Minoru Tanaka*

Department of Mathematics, Tokai University, Kanagawa, Japan

About this Article

Journal

Vol. 16 No. 1 (2016)

Type of Manuscript

Review Article

Keywords

Riemannian manifolds, surface of revolution, homeomorphic

Published

30 March 2018

The Cut Locus of Riemannian Manifolds: A Surface of Revolution

Abstract

How to Cite

References

Author Information

Minoru Tanaka*

About this Article

Journal

Type of Manuscript

Keywords

Published

Current Journal

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