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Pointwise conformal metrics

  • Paolo Mastrolia
  • Marco Rigoli
  • Alberto G. Setti
Chapter
  • 653 Downloads
Part of the Progress in Mathematics book series (PM, volume 302)

Abstract

At the beginning of this chapter we introduce the basic formalism and the derivation of the geometric Yamabe equation. Then, we concentrate on the case where M is compact to illustrate the interplay between geometry and analysis, with a few illuminating examples such as the Kazdan-Warner obstruction, a result of Obata on Einstein manifolds, the far-reaching generalization of Bidaut-V eron and Veron and a result of Escobar. Along the way we give a detailed proof, which inspires to P. Petersens treatise [Pet06a], of a famous rigidity result of Obata. In this way, we hope to provide some geometrical feeling on the subject of this monograph that will enable us to proceed with the noncompact case: the case of the rest of our investigation.

Keywords

Riemannian Manifold Scalar Curvature Constant Curvature Divergence Theorem Einstein Manifold 
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 Basel 2012

Authors and Affiliations

  • Paolo Mastrolia
    • 1
  • Marco Rigoli
    • 1
  • Alberto G. Setti
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi die MilanoMilanoItaly
  2. 2.Dipartimento di Fisica e MatematicaUniversità dell’InsubriaComoItaly

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