TY - BOOK ID - 5375571 TI - Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces PY - 2005 SN - 3764373717 3764374322 9783764373719 9786610460083 1280460083 PB - Basel : Birkhäuser Basel : Imprint: Birkhäuser, DB - UniCat KW - Functional equations. KW - Conformal geometry. KW - Lie algebras. KW - General relativity (Physics) KW - Equations fonctionnelles KW - Géométrie conforme KW - Algèbres de Lie KW - Relativité générale (Physique) KW - Complexes. KW - General relativity (Physics). KW - Geometry. KW - Mathematical physics. KW - Functional equations KW - Conformal geometry KW - Lie algebras KW - Complexes KW - Mathematics KW - Civil & Environmental Engineering KW - Physical Sciences & Mathematics KW - Engineering & Applied Sciences KW - Operations Research KW - Geometry KW - Géométrie conforme KW - Algèbres de Lie KW - Relativité générale (Physique) KW - EPUB-LIV-FT LIVMATHE SPRINGER-B KW - Relativistic theory of gravitation KW - Relativity theory, General KW - Linear complexes KW - Algebras, Lie KW - Circular geometry KW - Geometry of inverse radii KW - Inverse radii, Geometry of KW - Inversion geometry KW - Möbius geometry KW - Equations, Functional KW - Mathematics. KW - Physics. KW - Mathematical Methods in Physics. KW - Gravitation KW - Physics KW - Relativity (Physics) KW - Algebras, Linear KW - Coordinates KW - Line geometry KW - Transformations (Mathematics) KW - Algebra, Abstract KW - Lie groups KW - Functional analysis KW - Physical mathematics KW - Euclid's Elements KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics UR - https://www.unicat.be/uniCat?func=search&query=sysid:5375571 AB - 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. ER -