On Galilean 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 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.

Surjective Isometries on Grassmann Spaces

Let H be a complex Hilbert space, n a given positive integer and let Pn(H) be the set of all projections on H with rank n. Under the condition dimH ≥ 4n, we describe the surjective isometries of Pn(H) with respect to the gap metric (the metric induced by the operator norm).