Geometries and Transformations

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Norman W. JohnsonCambridge University Press, 6/7/2018EAN 9781107103405, ISBN10: 1107103401Hardcover, 350 pages, 24.1 x 16.2 x 2.7 cmLanguage: EnglishEuclidean 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.Introduction1. Homogenous spaces2. Linear geometries3. Circular geometries4. Real collineation groups5. Equiareal collineations6. Real isometry groups7. Complex spaces8. Complex collineation groups9. Circularities and concatenations10. Unitary isometry groups11. Finite symmetry groups12. Euclidean symmetry groups13. Hyperbolic coxeter groups14. Modular transformations15. Quaternionic modular groups. Show more