An Introduction to Lorentz Surfaces

Name: An Introduction to Lorentz Surfaces | Introduction to Lorentz Surfaces
Brand: De Gruyter
Price: 139.95 EUR
Availability: OnlineOnly

Introduction to Lorentz Surfaces

Tilla Weinstein(Autor*in)

De Gruyter (Verlag)

1. Auflage

Erschienen am 24. Juni 2011

XIII, 213 Seiten

E-Book

PDF mit Wasserzeichen-DRM

Systemvoraussetzungen

978-3-11-082163-5 (ISBN)

139,95 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Wasserzeichen-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Inhalt

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

Systemvoraussetzungen

Als PDF speichern Als Link merken