Geodesics on the unit tangent bundle

Author:

Berndt J.,Boeckx E.,Nagy P. T.,Vanhecke L.

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. SOME SPECIAL CURVES IN THE UNIT TANGENT BUNDLES OF SURFACES;Journal of Science and Arts;2022-06-30

2. Geometric Finite Elements;Handbook of Variational Methods for Nonlinear Geometric Data;2020

3. Submersions and curves of constant geodesic curvature;Mathematische Nachrichten;2019-05-21

4. Magnetic curves on tangent sphere bundles;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2018-11-20

5. Tensor tomography on Cartan–Hadamard manifolds;Inverse Problems;2018-03-16

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