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Recent Trends in Lorentzian Geometry

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Miguel Sánchez

    1. , Dept of Geometry and Topology, University of Granada, Granada, Spain

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  2. MIguel Ortega

    1. Departamento de Mátematica Aplicada, Universidad de Granada, Granada, Spain

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    You can also search for this editor in PubMed   Google Scholar

  3. Alfonso Romero

    1. , Dept. of Geometry and Topology, University of Granada, Granada, Spain

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  • Contains contributions from leaders in the field of Lorentzian Geometry
  • Presents material on pure and applied Lorentzian Geometry such as geodesics, submanifolds, causality, black holes, geometry of spacetimes or AdS-CFT correspondence
  • Serves differential geometers, mathematical physicists and relativists ?
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 26)

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Table of contents (15 papers)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Hyperbolic Metrics on Riemann Surfaces and Space-Like CMC-1 Surfaces in de Sitter 3-Space

    • Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada
    Pages 1-47

  3. Calabi–Bernstein Results and Parabolicity of Maximal Surfaces in Lorentzian Product Spaces

    • Alma L. Albujer, Luis J. Alías
    Pages 49-85

  4. Umbilical-Type Surfaces in SpaceTime

    • José M. M. Senovilla
    Pages 87-109

  5. Stability of Marginally Outer Trapped Surfaces and Applications

    • Marc Mars
    Pages 111-138

  6. Area Inequalities for Stable Marginally Trapped Surfaces

    • José Luis Jaramillo
    Pages 139-161

  7. Infinitesimal and Local Convexity of a Hypersurface in a Semi-Riemannian Manifold

    • Erasmo Caponio
    Pages 163-177

  8. Global Geodesic Properties of Gödel-type SpaceTimes

    • Rossella Bartolo, Anna Maria Candela, José Luis Flores
    Pages 179-193

  9. The Geometry of Collapsing Isotropic Fluids

    • Roberto Giambò, Giulio Magli
    Pages 195-205

  10. Conformally Standard Stationary SpaceTimes and Fermat Metrics

    • Miguel Angel Javaloyes
    Pages 207-230

  11. Can We Make a Finsler Metric Complete by a Trivial Projective Change?

    • Vladimir S. Matveev
    Pages 231-242

  12. The C-Boundary Construction of SpaceTimes: Application to Stationary Kerr SpaceTime

    • J. L. Flores, J. Herrera
    Pages 243-275

  13. On the Isometry Group of Lorentz Manifolds

    • Leandro A. Lichtenfelz, Paolo Piccione, Abdelghani Zeghib
    Pages 277-293

  14. Conformally Flat Homogeneous Lorentzian Manifolds

    • Kyoko Honda, Kazumi Tsukada
    Pages 295-314

  15. Polar Actions on Symmetric Spaces

    • José Carlos Díaz-Ramos
    Pages 315-334

  16. (para)-Kähler Weyl Structures

    • P. Gilkey, S. Nikčević
    Pages 335-353
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Keywords

About this book

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.

Editors and Affiliations

  • , Dept of Geometry and Topology, University of Granada, Granada, Spain

    Miguel Sánchez

  • Departamento de Mátematica Aplicada, Universidad de Granada, Granada, Spain

    MIguel Ortega

  • , Dept. of Geometry and Topology, University of Granada, Granada, Spain

    Alfonso Romero

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