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Non-closed isometry-invariant geodesics

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Abstract

Let c be a non-closed and bounded geodesic in a complete Riemannian manifold M. Assume that c is invariant under an isometry A of M and that c is not contained in the set of fixed points of A. We prove that, for some \({k\ge 2}\), the geodesic flow line ċ corresponding to c is dense in a k-dimensional torus N embedded in TM. In particular, every geodesic with initial vector in N is A-invariant.

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  1. Abteilung Reine Mathematik, Mathematisches Institut der Universität Freiburg, Eckerstr. 1, 79104, Freiburg, Germany

    Victor Bangert

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  1. Victor Bangert
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Correspondence to Victor Bangert.

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Bangert, V. Non-closed isometry-invariant geodesics. Arch. Math. 106, 573–580 (2016). https://doi.org/10.1007/s00013-016-0904-4

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  • DOI: https://doi.org/10.1007/s00013-016-0904-4

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