Symmetry Considerations, Topological Constraints, and Interactions with Physics

  • Seiki Nishikawa
  • Richard Schoen


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.


Modulus Space Variational Problem Einstein Metrics Einstein Manifold Symmetry Consideration 
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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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