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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 (j.berndt@maths.hull.ac.uk)
E. Boeckx
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium (eric.boeckx@wis.kuleuven.ac.be)
P. T. Nagy
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, PO Box 12, H-4010, Hungary (nagypeti@math.klte.hu)
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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.

Information

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

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