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Closed Geodesics on Compact Nilmanifolds with Chevalley Rational Structure

Rachelle DeCoste
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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.

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Rachelle DeCoste. 2007-03-30. Closed Geodesics on Compact Nilmanifolds with Chevalley Rational Structure. https://arxiv.org/abs/math/0703930

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