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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.
List of contents
Hyperbolic metrics on Riemann surfaces and spacelike CMC-1 surfaces in de Sitter 3-space, Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada. - Bernstein results and parabolicity of maximal surfaces in Lorentzian product spaces, Alma L. Albujer and Luis J. Alías, Calabi. - Umbilical-Type Surfaces in Spacetime, José M. M. Senovilla. - Stability of marginally outer trapped surfaces and applications, Marc Mars. - Area inequalities for stable marginally trapped surfaces, José Luis Jaramillo. - Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold, Erasmo Caponio. - Global geodesic properties of Gödel type spacetimes, R. Bartolo, A.M. Candela and J.L. Flores.- The geometry of collapsing isotropic fluids, Roberto Giamb`o and Giulio Magli. - Conformally standard stationary spacetimes and Fermat metrics, Miguel Ángel Javaloyes. - Can we make a Finsler metric complete by a trivial projective change? Vladimir S. Matveev. - The c-boundary construction of spacetimes: application to stationary Kerr spacetime, J.L. Flores and J. Herrera. - On the isometry group of Lorentz manifolds, Leandro A. Lichtenfelz, Paolo Piccione, and Abdelghani Zeghib. - Conformally flat homogeneous Lorentzian Manifolds, Kyoko Honda and Kazumi Tsukada. - Polar actions on symmetric spaces, José Carlos Díaz-Ramos. - (para)-Kähler Weyl structures, P. Gilkey and S. Nikcevic
Summary
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.
