Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T17:08:12.054Z Has data issue: false hasContentIssue false
  • English
  • Français

Geodesics on the unit tangent bundle

Published online by Cambridge University Press:  12 July 2007

J. Berndt ,
E. Boeckx ,
P. T. Nagy  and
L. Vanhecke
J. Berndt
Affiliation:
Department of Mathematics, University of Hull, Hull HU6 7RX, UK ([email protected])
E. Boeckx
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium ([email protected])
P. T. Nagy
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, PO Box 12, H-4010, Hungary ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

A geodesic γ on the unit tangent sphere bundle T1M of a Riemannian manifold (M, g), equipped with the Sasaki metric gS, can be considered as a curve x on M together with a unit vector field V along it. We study the curves x. In particular, we investigate for which manifolds (M, g) all these curves have constant first curvature κ1 or have vanishing curvature κi for some i = 1, 2 or 3.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 6 , December 2003 , pp. 1209 - 1229
Copyright
Copyright © Royal Society of Edinburgh 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)