April 23, 2021.

*Rigidity of Homogeneous Gradient Soliton Metrics and Related Equations.*

In this talk I’ll discuss structure results for homogeneous Riemannian spaces that support a non-constant solution to two general classes of equations involving the Hessian of a function. Our results generalize earlier rigidity results for gradient Ricci solitons and warped product Einstein metrics. In particular, they provide results for homogeneous gradient solitons of any invariant curvature flow and give a new structure result for homogeneous conformally Einstein metrics. This is joint work with P. Petersen of UCLA.