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lgli/290.pdf
Classical geometries in modern contexts : geometry of real inner product spaces 🔍
Walter Benz Birkhauser Basel, Boston, Mass, Massachusetts, 2005
英语 [en] · PDF · 2.3MB · 2005 · 📘 非小说类图书 · 🚀/lgli/lgrs · Save
描述
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.
备用文件名
lgrsnf/290.pdf
备选作者
Benz, Walter
备用出版商
Birkhäuser ; Springer [distributor
备用出版商
Birkhäuser Verlag
备用出版商
Birkhäuser Basel
备用出版商
Birkhäuser GmbH
备用版本
Basel, GW, Boston, MA, United States, 2006
备用版本
Basel ; Boston, ©2005
备用版本
Basel, London, 2006
备用版本
Germany, Germany
备用版本
1, 2005
元数据中的注释
Includes bibliographical references and index.
备用描述
Presents the real inner product spaces of arbitrary (finite or infinite) dimension greater than or equal to 2. This book studies the sphere geometries of Mobius and Lie for these spaces, besides euclidean and hyperbolic geometry, as well as geometries where Lorentz transformations play the key role
开源日期
2024-03-19
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