最 低 价：￥203.00
定 价：￥225.55
作 者：HerbertBusemann 著 著
出 版 社：Oversea Publishing House
出版时间：2005-5-1
I S B N：9780486442372
| Preface CHAPTER I. THE BASIC CONCEPTS 1. Introduction 2. Compact and finitely compact metric spaces 3. Convergence of point sets 4. Motion and isometry 5. Curves and their lengths 6. Segments 7. Geodesics 8. G-spaces 9. Multiplicity. Geodesics without multiple points 10. Two-dimensional G-spaces 11. Plane metrics without conjugate points CHAPTER II. DESAEGUESIAN SPACES 12. Introduction 13. Planes with the Desargues property 14. Spaces which contain planes 15. Fdemann and Finsler spaces. Beltrami's theorem 16. Convex sets in affine space 17. Minkowskian geometry 18. Hilbert's geometry CHAPTER III. PERPENDICULARS AND PARALLELS 19. Introduction 20. Convexity of spheres and perpendicularity 21. Characterization of the higher-dimensional elliptic geometry 22. Limit spheres and co-rays in G-spaces 23. Asymptotes and parallels in straight spaces 24. Characterizations of the higher-dimensional Minkowskian geometry 25. Characterization of the Minkowski plane CHAPTER IV. COVERING SPACES 26. Introduction 27. Locally isometric spaces 28. The universal covering space 29. Fundamental sets 30. Locally Minkowskian, hyperbohc, or spherical spaces 31. Spaces in which two points determine a geodesic 32. Free homotopy and closed geodesics 33. Metrics without conjugate points on the torus . 34. Transitive geodesics on surfaces of higher genus CHAPTER V. THE INFLUENCE OF THE SIGH OF THE CURVATURE ON THE GEODESICS 35. Introduction 36. Local properties 37. Non-positive curvature mtne theory ot parallels 38. Straightness of the universal covering space 39. The. fundamental groups of spaces with convex capsules 40. Geodesics in spaces with negative curvature 41. Relation to non-positive curvature in standard sense 42. Angular measure 43. Excess and characteristic 44. Simple monogons, total excess, surfaces with positive excess CHAPTER VI. HOMOGENEOUS SPACES 45. Introduction 46. Spaces with flat bisectors I 47. Spaces with fiat bisectors II 48. Applications of the bisector theorem. The Helmholtz-Lie Problem 49. Involutoric motions 50. New characterizations of the Minkowskian spaces 51. Translations along two lines 52. Surfaces with transitive groups of motions 53. The hermitian elliptic and similar spaces 54. Compact spaces with pairwise transitive groups of motions 55. Odd-dimensional spaces with pairwise transitive groups of motions APPENDIX Problems and Theorems NOTES TO THE TEXT INDEX |
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