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Closed geodesics on compact nilmanifolds with Chevalley rational structure

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Abstract

We study the distribution of closed geodesics on nilmanifolds Γ \ N arising from a 2-step nilpotent Lie algebra \({\mathfrak {N}}\) constructed from an irreducible representation of a compact semisimple Lie algebra \({\mathfrak {g}o}\) on a real finite dimensional vector space U. We determine sufficient conditions on the semisimple Lie algebra \({\mathfrak {g}o}\) for Γ \ N to have the density of closed geodesics property where Γ is a lattice arising from a Chevalley rational structure on \({\mathfrak{N}}\) .

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Correspondence to Rachelle C. DeCoste.

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DeCoste, R.C. Closed geodesics on compact nilmanifolds with Chevalley rational structure. manuscripta math. 127, 309–343 (2008). https://doi.org/10.1007/s00229-008-0206-7

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  • DOI: https://doi.org/10.1007/s00229-008-0206-7

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