Geodesics on the unit tangent bundle

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In this Subject: <a title="Mathematics and Statistics" href="/content/subcat?j_subject=195&j_availability=">Mathematics and Statistics
By this author: Berndt J. ;&nbsp; Boeckx E. ;&nbsp; Nagy P.T. ;&nbsp; Vanhecke L.

Authors: Berndt J.; Boeckx E.; Nagy P.T.; Vanhecke L.

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 133, Number 6, 19 December 2003 , pp. 1209-1229(21)

Publisher: Royal Society of Edinburgh

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Abstract:

A geodesic gamma

on the unit tangent sphere bundle T₁M of a Riemannian manifold (M, g), equipped with the Sasaki metric g_S, 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 kappa