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

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

2011-07-26

arxiv.org/abs/1107.5335v2

Mathematics

Differential Geometry

LaTeX2e, 28 pages, 1 figure

Scientific paper

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 one-parameter families of U(n+1), Sp(n+1) and Spin(9)-homogeneous metrics. In the process, we also describe the spectrum of the Laplacian of such metrics and compute its first eigenvalue.

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