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PreprintarXiv licencearXiv

Closed geodesics on compact semi-Riemannian manifolds

  • Souheib Allout
  • Salah Chaib
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Abstract

We study the existence of closed geodesics on compact quotients of Lie groups endowed with left-invariant pseudo-Riemannian metrics. We construct a compact, geodesically complete pseudo-Riemannian manifold that admits no closed geodesics. We also establish the existence of closed geodesics in several settings, with particular focus on the Lorentzian case.

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Cite

BibTeXRIS
BibTeX
@misc{allout2026closed,
  title = {{Closed geodesics on compact semi-Riemannian manifolds}},
  author = {Souheib Allout and Salah Chaib},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23552},
  eprint = {2610.23552},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23552},
}
RIS
TY  - UNPB
TI  - Closed geodesics on compact semi-Riemannian manifolds
AU  - Souheib Allout
AU  - Salah Chaib
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23552
UR  - https://arxiv.org/abs/2610.23552
AB  - We study the existence of closed geodesics on compact quotients of Lie groups endowed with left-invariant pseudo-Riemannian metrics. We construct a compact, geodesically complete pseudo-Riemannian manifold that admits no closed geodesics. We also establish the existence of closed geodesics in several settings, with particular focus on the Lorentzian case.
ER  -