Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces

Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces
Автор
 
Год
 
Страниц
 
251
ISBN
 
ISBN10:3764373717
Издатель
 
Birkhäuser Basel

Описание:

This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere geometries of M?bius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. The geometrical notions of this book are based on general spaces X as described. This implies that also mathematicians who have not so far been especially interested in geometry may study and understand great ideas of classical geometries in modern and general contexts. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry.

Похожие книги

Handbook of incidence geometry. Buildings and foundationsHandbook of incidence geometry. Buildings and foundations
Автор: Buekenhout F. (ed.)
Год: 1995
Functional AnalysisFunctional Analysis
Автор: Riesz F., Sz.-Nagy B.
Год: 1956
Finite Unitary Reflection GroupsFinite Unitary Reflection Groups
Автор: Shephard G.C., Todd J.A.
Backlund & Darboux TransformationsBacklund & Darboux Transformations
Автор: C. Rogers, W. K. Schief
Год: 2002