Closed Geodesics on Compact Nilmanifolds with Chevalley Rational Structure

2007/03/30 by DeCoste, Rachelle
#53C22 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0703930

Abstract

We continue the study of the distribution of closed geodesics on nilmanifolds constructed from a simply connected 2-step nilpotent Lie group with a left invariant metric and a lattice. We consider a Lie group with an associated 2-step nilpotent Lie algebra constructed from an irreducible representation of a compact semisimple Lie algebra on a real finite dimensional vector space. We determine sufficient conditions on the semisimple Lie algebra for the nilmanifold to have the density of closed geodesics property for a lattice arising from a Chevalley rational structure.

Related

• Some remarks on semi-classical analysis on two-step Nilmanifolds
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• Homogeneous geodesics in pseudo-Riemannian nilmanifolds
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