هندسهٔ ژئودزیک‌ها (ریاضیات خالص و کاربردی، جلد ششم)

Front Cover......Page 1 The Geometry of Geodesics......Page 4 Copyright Page......Page 5 Table of Contents......Page 10 Preface......Page 6 1. Introduction......Page 12 2. Compact and Finitely Compact Metric Spaces......Page 14 3. Convergence of Point Sets......Page 21 4. Motion and Isometry......Page 25 5. Curves and Their Lengths......Page 30 6. Segments......Page 38 7. Geodesics......Page 41 8. G-Spaces......Page 47 9. Multiplicity, Geodesics Without Multiple Points......Page 55 10. Two-Dimensional G-Spaces......Page 60 11. Plane Metrics Without Conjugate Points......Page 67 12. Introduction......Page 76 13. Planes with the Desargues Property......Page 77 14. Spaces Which Contain Planes......Page 87 15. Riemann and Finsler Spaces. Beltrami's Theorem......Page 93 16. Convex Sets in Affine Space......Page 98 17. Minkowskian Geometry......Page 105 18. Hilbert's Geometry......Page 116 19. Introduction......Page 126 20. Convexity of Spheres and Perpendicularity......Page 128 21. Characterization of the Higher-Dimensional Elliptic Geometry......Page 135 22. Limit Spheres and Co-Rays in G-Spaces......Page 141 23. Asymptotes and Parallels in Straight Spaces......Page 148 24. Characterizations of the Higher-Dimensional Minkowskian Geometry......Page 155 25. Characterization of the Minkowski Plane......Page 164 26. Introduction......Page 176 27. Locally Isometric Spaces......Page 178 28. The Universal Covering Space......Page 185 29. Fundamental Sets......Page 192 30. Locally Minkowskian, Hyperbolie or Spherical Spaces......Page 199 31. Spaces in Which Two Points Determine a Geodesic......Page 210 32. Free Homotopy and Closed Geodesics......Page 215 33. Metrics Without Conjugate Points on the Torus......Page 226 34. Transitive Geodesics on Surfaces of Higher Genus......Page 234 36. Introduction......Page 246 36. Local Properties......Page 248 37. Non-Positive Curvature in the Theory of Parallels......Page 259 38. Straightness of the Universal Covering Space......Page 265 39. The Fundamental Groups of Spaces with Convex Capsules......Page 269 40. Geodesics in Spaces with Negative Curvature......Page 273 41. Relation to Non-Positive Curvature in Standard Sense......Page 278 42. Angular Measure......Page 284 43. Excess and Characteristic......Page 293 44. Simple Monogons, Total Excess. Surfaces with Positive Excess......Page 303 45. Introduction......Page 318 46. Spaces with Flat Bisectors I......Page 320 47. Spaces with Flat Bisectors II......Page 331 48. Applications of the Bisector Theorem. The Helmholtz-Lie Problem......Page 344 49. Involutoric Motions......Page 354 50. New Characterizations of the Minkowskian Spaces......Page 361 51. Translations Along Two Lines......Page 370 52. Surfaces With Transitive Groups of Motions......Page 377 53. The Hermitian Elliptic and Similar......Page 385 54. Compact Spaces with Pairwise Transitive Groups of Motions......Page 396 55. Odd-Dimensional Spaces with Pairwise Transitive Groups of Motions......Page 405 Appendix . Problems and Theorems......Page 414 Notes of the Text......Page 424 Index......Page 428