The Large Scale Geometry of Nilpotent Lie Groups
نویسنده
چکیده
In this paper, we prove results concerning the large scale geometry of connected, simply connected nilpotent Lie groups equipped with left invariant Riemannian metrics. Precisely, we prove that there do not exist quasi-isometric embeddings of such a nilpotent Lie group into either a CAT0 metric space or an Alexandrov metric space. The main technical aspect of this work is the proof of a limited metric differentiability of Lipschitz maps between connected graded nilpotent Lie groups equipped with left invariant Carnot-Carathéodory metrics and complete metric spaces.
منابع مشابه
Some properties of nilpotent Lie algebras
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