38 citations · 41 across the 9 of their papers we have counts for
11 papers
Critical metrics of the volume functional on complete manifolds
Caio Coimbra, Rafael Diógenes, Ernani Ribeiro
In this article, we investigate critical metrics of the volume functional on complete manifolds without boundary. We prove that any critical metric of the volume functional on a co…
On quasi-Einstein manifolds with constant scalar curvature
Johnatan Costa, Ernani Ribeiro, Márcio Santos
In this article, we study quasi-Einstein manifolds with constant scalar curvature. We provide a classification of compact and noncompact (possibly with boundary) -flat quasi-Ein…
Geometric inequalities for quasi-Einstein manifolds
Rafael Diógenes, Jaciane Gonçalves, Ernani Ribeiro
In this article, we investigate certain geometric inequalities on quasi-Einstein manifolds. We use the generalized Reilly's formulas by Qiu-Xia and Li-Xia to establish new boundary…
Rigidity of compact quasi-Einstein manifolds with boundary
Johnatan Costa, Ernani Ribeiro, Detang Zhou
In this article, we investigate the geometry of compact quasi-Einstein manifolds with boundary. We show that a -dimensional simply connected compact quasi-Einstein manifold with…
Geometry of static perfect fluid space-time
Johnatan Costa, Rafael Diógenes, Neilha Pinheiro +1
In this article, we investigate the geometry of static perfect fluid space-time on compact manifolds with boundary. We use the generalized Reilly's formula to establish a geometric…
Four-dimensional complete gradient shrinking Ricci solitons
Huai-Dong Cao, Ernani Ribeiro, Detang Zhou
In this article, we study four-dimensional complete gradient shrinking Ricci solitons. We prove that a four-dimensional complete gradient shrinking Ricci soliton satisfying a point…
Noncompact quasi-Einstein manifolds conformal to a Euclidean space
Ernani Ribeiro, Keti Tenenblat
The goal of this article is to investigate nontrivial -quasi-Einstein manifolds globally conformal to an -dimensional Euclidean space. By considering such manifolds, whose co…
Geometric inequalities for critical metrics of the volume functional
H. Baltazar, R. Batista, E. Ribeiro
In this article, we investigate the geometry of critical metrics of the volume functional on an -dimensional compact manifold with (possibly disconnected) boundary. We establish…
Volume functional of compact -manifolds with a prescribed boundary metric
H. Baltazar, R. Diógenes, E. Ribeiro
We prove that a critical metric of the volume functional on a -dimensional compact manifold with boundary satisfying a second-order vanishing condition on the Weyl tensor must b…
Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary
H. Baltazar, E. Ribeiro
We provide a general Böchner type formula which enables us to prove some rigidity results for -static spaces. In particular, we show that an -dimensional positive static trip…
A note on the uniqueness of quasi-Einstein metrics on
E. Ribeiro, K. Bezerra
The aim of this note is to give an explicit description of quasi-Einstein metrics on We shall construct two examples of quasi-Einstein metrics on this…