Ebook: Recent Trends in Lorentzian Geometry
- Tags: Convex and Discrete Geometry, Hyperbolic Geometry, Differential Geometry
- Series: Springer Proceedings in Mathematics & Statistics 26
- Year: 2013
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques. Recent progress has attracted a renewed interest in this theory for many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and high energy physics have been found, and further connections with other geometries have been developed.
Samples of these fresh trends are presented in this volume, based on contributions from the VI International Meeting on Lorentzian Geometry, held at the University of Granada, Spain, in September, 2011. Topics such as geodesics, maximal, trapped and constant mean curvature submanifolds, classifications of manifolds with relevant symmetries, relations between Lorentzian and Finslerian geometries, and applications to mathematical physics are included.
This book will be suitable for a broad audience of differential geometers, mathematical physicists and relativists, and researchers in the field.Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques. Recent progress has attracted a renewed interest in this theory for many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and high energy physics have been found, and further connections with other geometries have been developed.
Samples of these fresh trends are presented in this volume, based on contributions from the VI International Meeting on Lorentzian Geometry, held at the University of Granada, Spain, in September, 2011. Topics such as geodesics, maximal, trapped and constant mean curvature submanifolds, classifications of manifolds with relevant symmetries, relations between Lorentzian and Finslerian geometries, and applications to mathematical physics are included. ?
This book will be suitable for a broad audience of differential geometers, mathematical physicists and relativists, and researchers in the field.
Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques. Recent progress has attracted a renewed interest in this theory for many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and high energy physics have been found, and further connections with other geometries have been developed.
Samples of these fresh trends are presented in this volume, based on contributions from the VI International Meeting on Lorentzian Geometry, held at the University of Granada, Spain, in September, 2011. Topics such as geodesics, maximal, trapped and constant mean curvature submanifolds, classifications of manifolds with relevant symmetries, relations between Lorentzian and Finslerian geometries, and applications to mathematical physics are included. ?
This book will be suitable for a broad audience of differential geometers, mathematical physicists and relativists, and researchers in the field.
Content:
Front Matter....Pages i-xii
Hyperbolic Metrics on Riemann Surfaces and Space-Like CMC-1 Surfaces in de Sitter 3-Space....Pages 1-47
Calabi–Bernstein Results and Parabolicity of Maximal Surfaces in Lorentzian Product Spaces....Pages 49-85
Umbilical-Type Surfaces in SpaceTime....Pages 87-109
Stability of Marginally Outer Trapped Surfaces and Applications....Pages 111-138
Area Inequalities for Stable Marginally Trapped Surfaces....Pages 139-161
Infinitesimal and Local Convexity of a Hypersurface in a Semi-Riemannian Manifold....Pages 163-177
Global Geodesic Properties of G?del-type SpaceTimes....Pages 179-193
The Geometry of Collapsing Isotropic Fluids....Pages 195-205
Conformally Standard Stationary SpaceTimes and Fermat Metrics....Pages 207-230
Can We Make a Finsler Metric Complete by a Trivial Projective Change?....Pages 231-242
The C-Boundary Construction of SpaceTimes: Application to Stationary Kerr SpaceTime....Pages 243-275
On the Isometry Group of Lorentz Manifolds....Pages 277-293
Conformally Flat Homogeneous Lorentzian Manifolds....Pages 295-314
Polar Actions on Symmetric Spaces....Pages 315-334
(para)-K?hler Weyl Structures....Pages 335-353
Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques. Recent progress has attracted a renewed interest in this theory for many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and high energy physics have been found, and further connections with other geometries have been developed.
Samples of these fresh trends are presented in this volume, based on contributions from the VI International Meeting on Lorentzian Geometry, held at the University of Granada, Spain, in September, 2011. Topics such as geodesics, maximal, trapped and constant mean curvature submanifolds, classifications of manifolds with relevant symmetries, relations between Lorentzian and Finslerian geometries, and applications to mathematical physics are included. ?
This book will be suitable for a broad audience of differential geometers, mathematical physicists and relativists, and researchers in the field.
Content:
Front Matter....Pages i-xii
Hyperbolic Metrics on Riemann Surfaces and Space-Like CMC-1 Surfaces in de Sitter 3-Space....Pages 1-47
Calabi–Bernstein Results and Parabolicity of Maximal Surfaces in Lorentzian Product Spaces....Pages 49-85
Umbilical-Type Surfaces in SpaceTime....Pages 87-109
Stability of Marginally Outer Trapped Surfaces and Applications....Pages 111-138
Area Inequalities for Stable Marginally Trapped Surfaces....Pages 139-161
Infinitesimal and Local Convexity of a Hypersurface in a Semi-Riemannian Manifold....Pages 163-177
Global Geodesic Properties of G?del-type SpaceTimes....Pages 179-193
The Geometry of Collapsing Isotropic Fluids....Pages 195-205
Conformally Standard Stationary SpaceTimes and Fermat Metrics....Pages 207-230
Can We Make a Finsler Metric Complete by a Trivial Projective Change?....Pages 231-242
The C-Boundary Construction of SpaceTimes: Application to Stationary Kerr SpaceTime....Pages 243-275
On the Isometry Group of Lorentz Manifolds....Pages 277-293
Conformally Flat Homogeneous Lorentzian Manifolds....Pages 295-314
Polar Actions on Symmetric Spaces....Pages 315-334
(para)-K?hler Weyl Structures....Pages 335-353
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