Prezada comunidade,

Nesta semana teremos a palestra do professor Willian Isao Tokura (Universidade Federal da Grande Dourados – UFGD).

Título: Gradient Einstein-type warped products: Rigidity, existence and nonexistence results via a nonlinear PDE
Data: 23 de outubro de 2025
Horário: 16h
Local: Auditório do DM

Resumo: In this talk, we establish the necessary and suficient conditions for constructing gradient Einstein-type warped metrics. One of these conditions leads us to a general Lichnerowicz equation with analytic and geometric coefficients for this class of metrics on the space of warping functions. In this way, we prove gradient estimates for positive solutions of a nonlinear elliptic differential equation on a complete Riemannian manifold with associated Bakry-Émery Ricci tensor bounded from below. As an application, we provide nonexistence and rigidity results for a large class of gradient Einstein-type warped metrics.