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arXiv · 2610.23552

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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Souheib Allout, Salah Chaib. 2026-10-16. Closed geodesics on compact semi-Riemannian manifolds. https://arxiv.org/abs/2610.23552

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