Koha online

Your cart is empty.
Normal view MARC view ISBD view

Classical Geometries in Modern Contexts [electronic resource] :Geometry of Real Inner Product Spaces / by Walter Benz.

by Benz, Walter [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Basel : Birkhäuser Basel, 2007.Edition: Second Edition.Description: online resource.ISBN: 9783764385415.Subject(s): Mathematics | Geometry | Mathematical physics | Mathematics | Geometry | Mathematical Methods in PhysicsDDC classification: 516 Online resources: Click here to access online
Contents:
Translation Groups -- Euclidean and Hyperbolic Geometry -- Sphere Geometries of Möbius and Lie -- Lorentz Transformations -- ?-Projective Mappings, Isomorphism Theorems.
In: Springer eBooksSummary: 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 Möbius 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.
Tags from this library: No tags from this library for this title. Add tag(s)
Log in to add tags.
    average rating: 0.0 (0 votes)

Translation Groups -- Euclidean and Hyperbolic Geometry -- Sphere Geometries of Möbius and Lie -- Lorentz Transformations -- ?-Projective Mappings, Isomorphism Theorems.

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 Möbius 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.

There are no comments for this item.

Log in to your account to post a comment.
@ Jomo Kenyatta University Of Agriculture and Technology Library

Powered by Koha