An Introduction to Lorentz Surfaces.

Intro -- Introduction -- Chapter 1. Null lines on Lorentz surfaces -- 1.1. Scalar products and causal character -- 1.2. Metrics and null direction fields -- 1.3. Lorentz surfaces and proper null coordinates -- 1.4. A first look at null lines -- 1.5. The Euclidean plane E2 and the Minkowski plane E21 -- Chapter 2. Box surfaces, yardsticks and global properties of Lorentzian metrics -- 2.1. The one-one correspondence between box surfaces and Lorentz surfaces -- 2.2. Yardsticks and time-orientability -- 2.3. Intrinsic curvature and a first look at the example in our logo -- 2.4. Geodesics and pregeodesics -- 2.5. Completeness, inextendibility, and causality conditions -- Chapter 3. Conformal equivalence and the Poincaré index -- 3.1. Definitions of conformal equivalence -- 3.2. Cj conformally equivalent Lorentz surfaces need not be Cj+1 conformally equivalent -- 3.3. The Poincaré index -- 3.4. The Poincaré Index Theorem -- Chapter 4 Kulkarni's conformal boundary -- 4.1. Ideal endpoints -- 4.2. The points on the conformal boundary -- 4.3. The topology on the conformal boundary -- 4.4. Some properties of the conformal boundary -- Chapter 5 Using the conformal boundary -- 5.1. The foliations X and Y -- 5.2. Spans on ℒ -- 5.3. A special ℋ+ chart on the span of a null curve -- 5.4. Characterization of C0 smoothability of the conformal boundary -- 5.5. Kulkarni's use of the conformal boundary -- Chapter 6. Conformal invariants on Lorentz surfaces -- 6.1. Conformal indices on an arbitrary Lorentz surface -- 6.2. Conformal indices associated with ∂ℒ and more properties of ∂ℒ -- 6.3. Some notions of symmetry -- 6.4. Smyth's digraph, determining sets and some other conformal invariants -- Chapter 7. Classical surface theory and harmonically immersed surfaces.

7.1. A quick review of local surface theory in Euclidean 3-space -- 7.2. A quick review of local surface theory in Minkowski 3-space -- 7.3. Contrasting the behavior of surfaces in E3 and E3,1 -- 7.4. The Hilbert-Holmgren theorem for harmonically immersed surfaces -- Chapter 8. Conformal realization of Lorentz surfaces in Minkowski 3-space -- 8.1. Entire timelike minimal surfaces in E3,1 -- 8.2. Associate families of minimal surfaces -- 8.3. Some conformal realizations of Lorentz surfaces in E3,1 -- 8.4. Some last remarks on conformal imbeddings and immersions -- Bibliography -- Index.

No detailed description available for "An Introduction to Lorentz Surfaces".

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.