Geometries and Transformations

封面
Cambridge University Press, 2018年6月7日 - 438 頁
Euclidean and other geometries are distinguished by the transformations that preserve their essential properties. Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the book builds on projective and inversive geometry to construct 'linear' and 'circular' geometries, including classical real metric spaces like Euclidean, hyperbolic, elliptic, and spherical, as well as their unitary counterparts. The first part of the book deals with the foundations and general properties of the various kinds of geometries. The latter part studies discrete-geometric structures and their symmetries in various spaces. Written for graduate students, the book includes numerous exercises and covers both classical results and new research in the field. An understanding of analytic geometry, linear algebra, and elementary group theory is assumed.
 

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內容

Preliminaries
1
Homogeneous Spaces
13
Linear Geometries
27
Circular Geometries
57
Real Collineation Groups
87
Equiareal Collineations
113
Real Isometry Groups
138
Complex Spaces
157
Complex Collineation Groups
168
Circularities and Concatenations
183
Unitary Isometry Groups
203
Finite Symmetry Groups
223
Tables
390
List of Symbols
406
Index
425
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關於作者 (2018)

Norman W. Johnson was Professor Emeritus of Mathematics at Wheaton College, Massachusetts. Johnson authored and co-authored numerous journal articles on geometry and algebra, and his 1966 paper 'Convex Polyhedra with Regular Faces' enumerated what have come to be called the Johnson solids. He was a frequent participant in international conferences and a member of the American Mathematical Society and the Mathematical Association of America.

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