Pointwise conformal metrics
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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.
KeywordsRiemannian Manifold Scalar Curvature Constant Curvature Divergence Theorem Einstein Manifold
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