On bifurcation of solutions of the Yamabe problem in product manifolds

Details On bifurcation of solutions of the Yamabe problem in product manifolds On bifurcation of solutions of the Yamabe problem in product manifolds

2010-12-07

arxiv.org/abs/1012.1497v2

Mathematics

Differential Geometry

22 pages, no figures. Revised version of October 18th, 2011: minor corrections, Remark 4.1 rewritten. To appear in Annales de

Scientific paper

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds.

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