Banca de DEFESA: VINICIUS ARAUJO DE MELO VALE

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE: VINICIUS ARAUJO DE MELO VALE
DATA: 28/07/2026
HORA: 15:00
LOCAL: PPGMAT-UFPI
TÍTULO: On the geometry of Bach-flat quasi-Einstein manifolds
PALAVRAS-CHAVES: Warped product; (\lambda, n+m)-Einstein manifolds; Well tensor; Bach tensor
PÁGINAS: 77
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
RESUMO:

In this dissertation, we study the geometric rigidity of compact $(\lambda,n+m)$- Einstein manifolds $(M^{n},g,f)$, $n\geq4,$ under the Bach-flat condition. Following the methodological approach of Chen and He, we analyze the behavior of the Weyl tensor and the potential function $f$ on these spaces. It is shown that the vanishing of the Bach tensor rigidly restricts the geometry of the manifold, implying that the space is locally conformally flat if $n=4, or that it has a harmonic Weyl tensor and zero radial Weyl curvature if $n\geq4$. Finally, we detail the global classification resulting from these properties for the case where the parametrer $m\neq1$ and the constant $\lambda$ is positive.

MEMBROS DA BANCA:
Presidente - 1728586 - HALYSON IRENE BALTAZAR
Interno - 1223720 - BRUNO VASCONCELOS MENDES VIEIRA
Externo à Instituição - 013.***.***-13 - ERNANI DE SOUSA RIBEIRO JÚNIOR - UFC