Geodesics on the unit tangent bundle

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 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 kappa1 or have vanishing curvature kappai for some i = 1, 2 or 3.

Document Type: Research article

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