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arXiv · 1107.5335

Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres

Renato G. Bettiol·Paolo Piccione
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Abstract

We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical points of the Hilbert-Einstein functional on such conformal classes, near homogeneous metrics. Both bifurcation and local rigidity type phenomena are obtained for 1-parameter families of U(n+1), Sp(n+1) and Spin(9)-homogeneous metrics.

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Renato G. Bettiol, Paolo Piccione. 2011-07-26. Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres. https://doi.org/10.1007/s00526-012-0535-y

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