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(2009 / vol.11 / no.1)
Density of Closed geodesics in two step Nilmanifolds
Changrim Jang , Keun Park
Pages. 33-40   



Let $M$ be a compact Riemannian manifold. It is very Interesting to know how many closed geodesic there are in the manifold $M$. The manifold $M$ is said to have the density of closed geodesics if the set of closed geodesics in $M$ is dense. In this survey, we will give some progress in the problem related to the density of closed geodesics in two step nilmanifolds.
The most results introduced in this paper are in cite{K}, cite{E}, cite{M}, cite{D},cite{LP} and cite{JP}.



1. Closed Geodesics and Density of Closed Geodesics
2. two step nilpotent metric groups
3. Geodesic equations in the two step nilpotent metric group



Two step nilpotent group, Closed geodesic



53C30, 22E25