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An introduction to Lorentz surfaces

Author: Tilla Weinstein
Publisher: Berlin ; New York : Walter de Gruyter, 1996.
Series: De Gruyter expositions in mathematics, 22.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic book
Electronic books
Additional Physical Format: Print version:
Weinstein, Tilla, 1934-
Introduction to Lorentz surfaces.
Berlin ; New York : Walter de Gruyter, 1996
(DLC) 95040470
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Tilla Weinstein
ISBN: 9783110821635 311082163X
OCLC Number: 811375606
Description: 1 online resource (xiii, 213 pages) : illustrations.
Contents: ""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 Kulkarniâ€?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 â??""; "" 5.3. A special â??+ chart on the span of a null curve""; "" 5.4. Characterization of C0 smoothability of the conformal boundary""; "" 5.5. Kulkarniâ€?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 â??â?? and more properties of â??â??"""" 6.3. Some notions of symmetry""; "" 6.4. Smythâ€?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""
Series Title: De Gruyter expositions in mathematics, 22.
Other Titles: Lorentz surfaces
Responsibility: by Tilla Weinstein.

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"The reviewer would recommend this monograph to anyone looking for an introduction to the geometry of Lorentz surfaces and especially to Kulkarni's conformal boundary for a Lorentz surface." Read more...

 
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