Foundations of incidence geometry : projective and polar spaces
Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces. Embedded into the modern view of diagram geometry, projective and...
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| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Izdaja: | 1st ed. 2011. |
| Serija: | Springer Monographs in Mathematics
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| Teme: | |
| Online dostop: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Sporočilo: |
Description d'après consultation du 18 février 2013 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Foundations of incidence geometry, projective and polar spaces, Johannes Ueberberg, Heidelberg, Springer, 2011, 1 vol. (XII-248 p.), Springer Monographs in mathematics, 978-3-642-20971-0 |
Kazalo:
- I Projective and Affine Geometries 1. Introduction 2. Geometries and Pregeometries 3. Projective and Affine Planes 4. Projective Spaces 5. Affine Spaces 6. A Characterization of Affine Spaces 7. Residues and Diagrams 8. Finite geometries II Isomorphisms and Collineations 1. Introduction 2. Morphisms 3. Projections 4. Collineations of projective and affine spaces 5. Central Collineations 6. The Theorem of Desargues III Projective Geometry over a Vector Space 1. Introduction 2. The Projective Space P(V) 3. Homogeneous Coordinates of Projective Spaces 4. Automorphisms of P(V) 5. The Affine Space AG(W) 6. Automorphisms of A(W) 7. The First Fundamental Theorem 8. The Second Fundamental Theorem IV Polar Spaces and Polarities 1. Introduction 2. The Theorem of Buekenhout-Shult 3. The diagram of a polar space 4. Polarities 5. Sesquilinear Forms 6. Pseudo-quadrics 7. The Kleinian Polar Space 8. The Theorem of Buekenhout and Parmentier V Quadrics and Quadratic Sets 1. Introduction 2. Quadratic Sets 3. Quadrics 4. Quadratic Sets in PG(3, K) 5. Perspective Quadratic Sets 6. Classification of the Quadratic Sets 7. The Kleinian Quadric 8. The Theorem of Segre 9. Further Reading References Index.