Extensions of distance preserving mappings in euclidean and hyperbolic geometry |
| |
Authors: | Walter Benz |
| |
Institution: | (1) Mathematisches Seminar, Universität Hamburg, Bundesstr. 55, 20146 Hamburg, Germany |
| |
Abstract: | Suppose that X is a real inner product
space of (finite or infinite) dimension at least 2. A distance preserving mapping
, where
is a (finite or infinite) subset of a
finite-dimensional subspace of X, can be extended
to an isometry
of X. This holds true for
euclidean as well as for hyperbolic geometry. To both geometries there exist examples
of non-extentable distance preserving
, where S
is not contained in a finite-dimensional subspace of
X. |
| |
Keywords: | 51M10 51F25 39B52 |
本文献已被 SpringerLink 等数据库收录! |
|