Special groups of isometries
We now analyze the action of some special groups of isometries acting on a Hadamard manifold X or more generally on a convex subset M ⊂ X. A group Γ operates discretely if for any compact set K ⊂ X there are only finitely many γ ∈ Γ with γK ∩ K ≠ φ. Γ operates freely (fixed point free), if γ does not contain nontrivial elliptic elements.
KeywordsNilpotent Group Semisimple Element Common Axis Affine Subspace Elliptic Element
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