A nonlinear Poisson transform for Einstein metrics on product spaces

Olivier Biquard (1, 2) , Rafe Mazzeo (3)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 Stanford University

We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If M is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein metrics is parametrized by certain new geometric structures on the Furstenberg boundary of M.

Domaines: Géométrie différentielle [math.DG]

Olivier Biquard, Rafe Mazzeo. A nonlinear Poisson transform for Einstein metrics on product spaces. Journal of the European Mathematical Society, 2011, 13, 5, pp.1423-1475. ⟨10.4171/JEMS/285⟩. ⟨hal-02928853⟩