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Symmetry Considerations, Topological Constraints, and Interactions with Physics

  • Seiki Nishikawa
  • Richard Schoen

Abstract

We begin this section by considering in Sub-Section A the simplest case of symmetries, i.e., when a group acts on the space of geometric objects and preserves the functional. When the group of invariance is infinite dimensional, this has deep consequences on the Euler-Lagrange equations of the Geometric Variational Problem. In Sub-Section B, we recall the Principle of Symmetric Criticality, and explain some of its consequences. We devote the next Sub-Section C to Conservation Laws that represent a subtle way in which symmetry considerations can affect a Geometric Variational Problem, in particular if the group involved is non compact.

Keywords

Modulus Space Variational Problem Einstein Metrics Einstein Manifold Symmetry Consideration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 1996

Authors and Affiliations

  • Seiki Nishikawa
    • 1
  • Richard Schoen
    • 2
  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan
  2. 2.Department of MathematicsStanford UniversityStanfordUSA

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