An Introduction to Lorentz Surfaces
eBook - PDF

An Introduction to Lorentz Surfaces

  1. 226 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

An Introduction to Lorentz Surfaces

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Yes, you can access An Introduction to Lorentz Surfaces by Tilla Weinstein in PDF and/or ePUB format, as well as other popular books in Mathematics & Geometry. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2011
Print ISBN
9783110143331
eBook ISBN
9783110821635
Edition
1
Topic
Mathematics
Subtopic
Geometry
Index
Mathematics

Table of contents

  1. Introduction
  2. Chapter 1. Null lines on Lorentz surfaces
  3. § 1.1. Scalar products and causal character
  4. § 1.2. Metrics and null direction fields
  5. § 1.3. Lorentz surfaces and proper null coordinates
  6. § 1.4. A first look at null lines
  7. § 1.5. The Euclidean plane E2 and the Minkowski plane E21
  8. Chapter 2. Box surfaces, yardsticks and global properties of Lorentzian metrics
  9. § 2.1. The one-one correspondence between box surfaces and Lorentz surfaces
  10. § 2.2. Yardsticks and time-orientability
  11. § 2.3. Intrinsic curvature and a first look at the example in our logo
  12. § 2.4. Geodesics and pregeodesics
  13. § 2.5. Completeness, inextendibility, and causality conditions
  14. Chapter 3. Conformal equivalence and the Poincaré index
  15. § 3.1. Definitions of conformal equivalence
  16. § 3.2. Cj conformally equivalent Lorentz surfaces need not be Cj+1 conformally equivalent
  17. § 3.3. The Poincaré index
  18. § 3.4. The Poincaré Index Theorem
  19. Chapter 4 Kulkarni’s conformal boundary
  20. § 4.1. Ideal endpoints
  21. § 4.2. The points on the conformal boundary
  22. § 4.3. The topology on the conformal boundary
  23. § 4.4. Some properties of the conformal boundary
  24. Chapter 5 Using the conformal boundary
  25. § 5.1. The foliations X and Y
  26. § 5.2. Spans on ℒ
  27. § 5.3. A special ℋ+ chart on the span of a null curve
  28. § 5.4. Characterization of C0 smoothability of the conformal boundary
  29. § 5.5. Kulkarni’s use of the conformal boundary
  30. Chapter 6. Conformal invariants on Lorentz surfaces
  31. § 6.1. Conformal indices on an arbitrary Lorentz surface
  32. § 6.2. Conformal indices associated with ∂ℒ and more properties of ∂ℒ
  33. § 6.3. Some notions of symmetry
  34. § 6.4. Smyth’s digraph, determining sets and some other conformal invariants
  35. Chapter 7. Classical surface theory and harmonically immersed surfaces
  36. § 7.1. A quick review of local surface theory in Euclidean 3-space
  37. § 7.2. A quick review of local surface theory in Minkowski 3-space
  38. § 7.3. Contrasting the behavior of surfaces in E3 and E3,1
  39. § 7.4. The Hilbert-Holmgren theorem for harmonically immersed surfaces
  40. Chapter 8. Conformal realization of Lorentz surfaces in Minkowski 3-space
  41. § 8.1. Entire timelike minimal surfaces in E3,1
  42. § 8.2. Associate families of minimal surfaces
  43. § 8.3. Some conformal realizations of Lorentz surfaces in E3,1
  44. § 8.4. Some last remarks on conformal imbeddings and immersions
  45. Bibliography
  46. Index