Closed geodesics in compact nilmanifolds

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Abstract

We study the density of closed geodesies property on 2-step nilmanifolds Γ \ N, where N is a simply connected 2-step nilpotent Lie group with a left invariant Riemannian metric and Lie algebra n-fraktur sign, and Γ is a lattice in N. We show the density of closed geodesics property holds for quotients of singular, simply connected, 2-step nilpotent Lie groups N which are constructed using irreducible representations of the compact Lie group SU (2).

Original languageEnglish
Pages (from-to)283-310
Number of pages28
JournalManuscripta Mathematica
Volume105
Issue number3
DOIs
StatePublished - Jul 2001

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