O Programa de Pós-Graduação em Matemática e Estatística convida a comunidade acadêmica a participar da palestra intitulada: “Divergence Identity for the scalar curvature and Rigidity of Codazzi Tensors”, a qual será ministrada no próximo dia 25/02/2026 (Quarta-Feira), às 10 horas, na Sala de aula do PPGME (ICEN/UFPA), com o Prof. Dr. Zhou Detang, da Universidade Federal Fluminense.

Resumo:

In this joint work with Xu Cheng and Andrés Lipa we introduce a local vector field on an $n$-dimensional Riemannian manifold, defined as the sum of the covariant derivatives of a local orthonormal frame,  and derive an explicit identity for its divergence, decomposed into a scalar curvature term and an auxiliary term involving connection coefficients. This result is applied to rigidity problems for Codazzi symmetric tensors. In particular, we give a new proof of a Tang-Yan theorem, which states that on a  closed $n$-dimensional manifold with nonnegative scalar curvature, a smooth Codazzi symmetric tensor whose trace invariants up to order $n-1$ are constant must have constant eigenvalues. We also obtain further rigidity results under assumptions on elementary symmetric functions of the eigenvalues, with applications to the isoparametric rigidity of closed hypersurfaces in the unit sphere.