Projective Geometry and Projective Metrics

Name: Projective Geometry and Projective Metrics | Projective Geometry and Projective Metrics
Brand: Academic Press
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Academic Press

Erschienen am 29. August 2011

331 Seiten

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978-0-08-087311-4 (ISBN)

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Front Cover
Projective Geometry and Projective Metrics
Copyright Page
TABLE OF CONTENTS
Preface
Chapter I. The Projective Plane
I. 1. Ideal Points
I. 2. The Projective Plane
I. 3. Projective Coordinates
I. 4. The Content of Projective Geometry. Duality Principle
I. 5. Groups of Transformations. Projectivities
I. 6. Cross Ratio . Intervals
I. 7. Perspectivities
I. 8. The Projectivities of Line on Itself
I. 9. Collineations
Exercises
Chapter II. Polarities And Conic Sections
II. 10. Polarities
II. 11. Conic Sections
II. 12. The Theorems of Steiner and Pascal
II. 13. Collineations of Conics
II. 14. Pencils of Conics
Exercises
Chapter III. Affine Geometry
III. 15. The Content of Affine Geometry . The Affine Group
III. 16. The Affine Theory of Conics
III. 17. Convex Sets
III. 18. The Equiaffine Group . Area
Exercises
Chapter IV. Projective Metrics
IV. 19. Metric Spaces
IV. 20. Segment, Straight Lines, Great Circles . Projective- Metric Spaces
IV. 21. Perpendiculars in Open Two-Spaces
IV. 22. Motions
IV. 23. Motions of Open Two-Spaces
IV. 24. Minkowskian Geometry
IV. 25. Reflections in Minkowskian Geometry . Euclidean Geometry
IV. 26. Angles and Motions in Euclidean Geometry
IV. 27. The Euclidean Theory of Conics
IV. 28. Hilbert's Geometry
IV. 29. Motions and Area in Hilbert Geometry . Definition of Hyperbolic Geometry
Exercises
Chapter V. Non-Euclidean Geometry
V. 30. Hyperbolic Trigonometry
V. 31. Length and Area
V. 32. Equidistant Curves and Limit Circles
V. 33. Some Synthetic Properties of Hyperbolic Geometry
V. 34. The Group of Hyperbolic Motions
V. 35. Weierstrass Coordinates
V. 36. Definition of Elliptic Geometry
V. 37. Elliptic Trigonometry . Relation of Elliptic and Spherical Geometry
V. 38. The Elliptic Line Element . Length and Area
V. 39. Cayley's Method
Exercises
Chapter VI. Spatial Geometry
VI. 40. Three-Dimensional Projective Space
VI. 41. Collineations of the Projective Space
VI. 42. Line Coordinates . Linear Complexes
VI. 43. Polarities and Quadrics
VI. 44. Linear Congruences and Reguli
VI. 45. Affine Geometry in Space
VI. 46. Convex Sets in Space
VI. 47. Three-Dimensional Projective-Metrics
VI. 48. Minkowskian Geometry in Space
VI. 49. Euclidean Geometry in Space
VI. 50. Hilbert's Geometry in Space . Hyperbolic Geometry
VI. 51. Hyperbolic Spheres, Limit Spheres, and Equidistant Surfaces
VI. 52. The Hyperbolic Group of Motions
VI. 53. Elliptic Geometry in Space
VI. 54. The Line Element of Elliptic Space
Bibliography
Index

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