On commuting isometries

On Galilean Isometries

Quite recently, Carter and Khalatnikov [CK] have pointed out that a geometric fourdimensional formulation of the non relativistic Landau theory of perfect superfluid dynamics should involve not only Galilei covariance but also, more significantly as far as gravitational effects are concerned, covariance under a larger symmetry group which they call the Milne group after Milne’s pioneering work ...

Isometries and Approximate Isometries

Some properties of isometric mappings as well as approximate isometries are studied. 2000 Mathematics Subject Classification. Primary 46B04. 1. Isometry and linearity. Mazur and Ulam [17] proved the following well-known result concerning isometries, that is, transformations which preserve distances. Theorem 1.1. Given two real normed vector spaces X and Y , let U be a surjective mapping from X ...

On Commuting and Non-Commuting Complexes

In this paper we study various simplicial complexes associated to the commutative structure of a finite group G. We define NC(G) (resp. C(G)) as the complex associated to the poset of pairwise non-commuting (resp. commuting) sets of nontrivial elements in G. We observe that NC(G) has only one positive dimensional connected component, which we call BNC(G), and we prove that BNC(G) is simply conn...

On Isometries of Square Sets

A Remark on Quasi-isometries

We show that if f : Bn -IRn is an e-quasi-isometry, with e < 1, defined on the unit ball Bn of Rn, then there is an affine isometry h : Bn -Rn with lIf(x) -h(x)|I < Ce(l+logn) where C is a universal constant. This result is sharp.