Recent Trends in Lorentzian GeometryMiguel Sánchez, Miguel Ortega, Alfonso Romero 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. |
Contents
1 | |
CalabiBernstein Results and Parabolicity of Maximal Surfaces in Lorentzian Product Spaces | 49 |
UmbilicalType Surfaces in SpaceTime | 86 |
Stability of Marginally Outer Trapped Surfaces and Applications | 111 |
Area Inequalities for Stable Marginally Trapped Surfaces | 139 |
Infinitesimal and Local Convexity of a Hypersurfacein a SemiRiemannian Manifold | 162 |
Global Geodesic Properties of Gödeltype SpaceTimes | 179 |
The Geometry of Collapsing Isotropic Fluids | 194 |
Conformally Standard Stationary SpaceTimes and Fermat Metrics | 207 |
Can We Make a Finsler Metric Complete by a Trivial ProjectiveChange? | 231 |
The CBoundary Construction of SpaceTimes Applicationto Stationary Kerr SpaceTime | 243 |
On the Isometry Group of Lorentz Manifolds | 276 |
Conformally Flat Homogeneous Lorentzian Manifolds | 295 |
Polar Actions on Symmetric Spaces | 315 |
paraKähler Weyl Structures | 335 |
Other editions - View all
Recent Trends in Lorentzian Geometry Miguel Sánchez,Miguel Ortega,Alfonso Romero No preview available - 2012 |
Recent Trends in Lorentzian Geometry Miguel Sánchez,Miguel Ortega,Alfonso Romero No preview available - 2014 |