Geodesics orbiting a singularity

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Authors

  • Daniel Grieser
  • Jørgen Olsen Lye

Research Organisations

External Research Organisations

  • Carl von Ossietzky University of Oldenburg
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Details

Original languageEnglish
Article number1
JournalJournal of Geometry
Volume115
Issue number1
Publication statusPublished - 9 Dec 2023

Abstract

We study the behaviour of geodesics on a Riemannian manifold near a generalized conical or cuspidal singularity. We show that geodesics entering a small neighbourhood of the singularity either hit the singularity or approach it to a smallest distance δ and then move away from it, winding around the singularity a number of times. We study the limiting behaviour δ→ 0 in the second case. In the cuspidal case the number of windings goes to infinity as δ→ 0 , and we compute the precise asymptotic behaviour of this number. The asymptotics have explicitly given leading term determined by the warping factor that describes the type of cuspidal singularity. We also discuss in some detail the relation between differential and metric notions of conical and cuspidal singularities.

Keywords

    Conical singularity, Cuspidal singularity, Geodesics, Singular hamiltonian systems

ASJC Scopus subject areas

Cite this

Geodesics orbiting a singularity. / Grieser, Daniel; Lye, Jørgen Olsen.
In: Journal of Geometry, Vol. 115, No. 1, 1, 09.12.2023.

Research output: Contribution to journalArticleResearchpeer review

Grieser, D., & Lye, J. O. (2023). Geodesics orbiting a singularity. Journal of Geometry, 115(1), Article 1. https://doi.org/10.48550/arXiv.2304.02895, https://doi.org/10.1007/s00022-023-00701-6
Grieser D, Lye JO. Geodesics orbiting a singularity. Journal of Geometry. 2023 Dec 9;115(1):1. doi: 10.48550/arXiv.2304.02895, 10.1007/s00022-023-00701-6
Grieser, Daniel ; Lye, Jørgen Olsen. / Geodesics orbiting a singularity. In: Journal of Geometry. 2023 ; Vol. 115, No. 1.
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