A simply connected nilpotent Lie group with a closed geodesic

Glen Wheeler

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arXiv · 2607.04678

A simply connected nilpotent Lie group with a closed geodesic

Glen Wheeler

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Abstract

We give a six-dimensional simply connected nilpotent Lie group together with a left-invariant Riemannian metric admitting a nonconstant closed geodesic. The example gives a positive answer to B\"ohm--Lafuente's question asking whether a homogeneous Riemannian manifold diffeomorphic to Euclidean space can have a closed geodesic.

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Glen Wheeler. 2026-07-06. A simply connected nilpotent Lie group with a closed geodesic. https://arxiv.org/abs/2607.04678

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