On isometries of Euclidean spaces

On Isometries of Euclidean Spaces

Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings

for all x ∈ X . Quasi-isometries occur naturally in the study of the geometry of discrete groups since the length spaces on which a given finitely generated group acts cocompactly and properly discontinuously by isometries are quasi-isometric to one another [Gro]. Quasi-isometries also play a crucial role in Mostow’s proof of his rigidity theorem: the theorem is proved by showing that equivaria...

Factoring Euclidean isometries

Every isometry of a finite dimensional euclidean space is a product of reflections and the minimum length of a reflection factorization defines a metric on its full isometry group. In this article we identify the structure of intervals in this metric space by constructing, for each isometry, an explicit combinatorial model encoding all of its minimal length reflection factorizations. The model ...

Euclidean Isometries and Surfaces

In this paper, we attempt a classification of the euclidean isometries and surfaces. Using isometry groups, we prove the Killing-Hopf theorem, which states that all complete, connected euclidean spaces are either a cylinder, twisted cylinder, torus, or klein bottle.

On Intrinsic Isometries to Euclidean Space

Compact metric spaces that admit intrinsic isometries to the Euclidean d-space are considered. Roughly, the main result states that the class of such spaces coincides with the class of inverse limits of Euclidean d-polyhedra. §