Closed Geodesics on Compact Nilmanifolds with Chevalley Rational Structure

Details Closed Geodesics on Compact Nilmanifolds with Chevalley Rational Structure Closed Geodesics on Compact Nilmanifolds with Chevalley Rational Structure

2007-03-30

arxiv.org/abs/math/0703930v1

Mathematics

Differential Geometry

39 pages, 3 tables

Scientific paper

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.

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