A characterization of orthogonality

Link:

https://doi.org/10.1007/s00022-009-2123-7

Autor/in:

Benz, Walter

Erscheinungsjahr:

2009

Medientyp:

Text

Schlagworte:

Dimension-free geometries
Euclidean and hyperbolic geometries

Beschreibung:

Let X be a real inner product space of (finite or infinite) dimension greater than one. We proved (see Theorem 7, Chapter 1 of our book [1]) that if T is a separable translation group of X, and d an appropriate distance function of X which is supposed to be invariant under T and the orthogonal group O of X, then there are, up to isomorphism, exactly two solutions of geometries (X,G(T,O)), G the group generated by T O, namely euclidean and hyperbolic geometry over X. With the same geometrical definition for both geometries of arbitrary (finite or infinite) dimension > 1 we will characterize in this note the notion of orthogonality. © 2009 Birkhäuser Verlag Basel/Switzerland.

Lizenz:

info:eu-repo/semantics/closedAccess

Quellsystem:

Forschungsinformationssystem der UHH

Interne Metadaten

Quelldatensatz: oai:www.edit.fis.uni-hamburg.de:publications/1ea25880-1417-4417-a4f2-bfd7958f6f70