Integrable geodesic flows on tubular sub-manifolds

Thomas Waters

doi:10.15673/tmgc.v10i3-4.770

Integrable geodesic flows on tubular sub-manifolds

Thomas Waters

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Abstract

In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dimensional manifolds, and using Jacobi fields we derive conditions under which the metric of the generalized tubular sub-manifold admits an ignorable coordinate. Some examples are given, demonstrating that these special surfaces can be quite elaborate and varied.

Original language	English
Pages (from-to)	17-28
Number of pages	12
Journal	Proceedings of the International Geometry Center
Volume	10
Issue number	3-4
DOIs	https://doi.org/10.15673/tmgc.v10i3-4.770
Publication status	Published - 20 Jan 2018

Keywords

geodesics
integrability
manifolds
Jacobi field
tube

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10.15673/tmgc.v10i3-4.770

770-1816-1-PBFinal published version, 683 KBLicence: CC BY

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AB - In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dimensional manifolds, and using Jacobi fields we derive conditions under which the metric of the generalized tubular sub-manifold admits an ignorable coordinate. Some examples are given, demonstrating that these special surfaces can be quite elaborate and varied.

KW - geodesics

KW - integrability

KW - manifolds

KW - Jacobi field

KW - tube

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JO - Proceedings of the International Geometry Center

JF - Proceedings of the International Geometry Center

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Integrable geodesic flows on tubular sub-manifolds

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Keywords

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