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

By R. G. Bettiol, Paolo Piccione. Calculus of Variations and Partial Differential Equations, 2011

47 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b8bbd76f5957546e0058c942226f8272095ea1a2