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Titlebook: Classical Geometries in Modern Contexts; Geometry of Real Inn Walter Benz Book 20072nd edition Birkh?user Basel 2007 Classical geometry.Fin

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發(fā)表于 2025-3-21 18:18:14 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Classical Geometries in Modern Contexts
副標(biāo)題Geometry of Real Inn
編輯Walter Benz
視頻videohttp://file.papertrans.cn/228/227074/227074.mp4
概述Dimension-free presentation.Inclusion of proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses.Common presentation for finite and infinite dimensional re
圖書封面Titlebook: Classical Geometries in Modern Contexts; Geometry of Real Inn Walter Benz Book 20072nd edition Birkh?user Basel 2007 Classical geometry.Fin
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 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..
出版日期Book 20072nd edition
關(guān)鍵詞Classical geometry; Finite; Hyperbolic geometry; Inner product space; Lie; Lorentz transformation; Natural
版次2
doihttps://doi.org/10.1007/978-3-7643-8541-5
isbn_ebook978-3-7643-8541-5
copyrightBirkh?user Basel 2007
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Book 20072nd edition(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. Th
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Translation Groups,hers we shall use later on, see the section . of this book. Instead of . (.) we will write . or, occasionally, .. The laws above are then the following: . for all . ∈ ., λ ∈ ?, and .:= . > 0 for all . ∈ .{0}. Instead of (.) we mostly will speak of ., hence tacitly assuming that . is equipped with a
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-Projective Mappings, Isomorphism Theorems, we do not exclude the case that there exist infinite linearly independent subsets of . or .. One of the important results of this chapter is that the hyperbolic geometries (.(.)), (.(.)) over . = (.), . = (.), respectively, . the group of hyperbolic motions, are isomorphic (see p. 16f) if, and only
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