26 mar 2026 -- 15:00
Aula Consulenze, Politecnico di Torino
Abstract.
Manifolds with density, also known as smooth metric measure spaces, arise through the modification of the standard Riemannian volume element of a Riemannian manifold (M,g) via the introduction of a smooth density function f. Notions of manifolds with density appear in numerous contexts (geometric flows, functional inequalities…), and they give rise to well-known weighted structures such as gradient Ricci solitons or quasi-Einstein metrics, among others. In this talk, we will go over some classification results for weighted Einstein manifolds, a natural generalization of quasi-Einstein metrics, under conditions on weighted objects related to the conformal behavior of manifolds with density. In particular, we will discuss a harmonicity condition on the weighted Weyl tensor, and the geometry of weighted conformal classes admitting several nonhomothetic weighted Einstein structures. This is joint work with Miguel Brozos-Vázquez and Eduardo García-Río.