arXiv subjects

Abdênago Barros

Publications and source records attributed to Abdênago Barros.

4 recordsLinked to original sources

arXiv2022

A local rigidity theorem for minimal two-spheres in an electrovacuum spacetime

The purpose of this article is to prove that, under suitable constrains on the electrovacuum spacetime $M$, if $Σ\subset M$ is an embedded strictly stable minimal two-sphere which locally maximizes the charged Hawking mass, then there exist a neighborhood of it in $M$ isometric to the Reissner-Nordström-de Sitter space. At the same time, motived by \cite{Brendle}, we will deduce an estimate for area of a two-sphere which is locally area minimizing in an electrovacuum spacetime. Moreover, if the equality holds, then there exist a neighborhood of it in $M$ isometric to the charged Nariai space.

math.DG↗

arXiv2013

Compact almost Ricci solitons with constant scalar curvature are gradient

The aim of this note is to prove that any compact non-trivial almost Ricci soliton $\big(M^n,\,g,\,X,\,λ\big)$ with constant scalar curvature is isometric to a Euclidean sphere $\Bbb{S}^{n}$. As a consequence we obtain that every compact non-trivial almost Ricci soliton with constant scalar curvature is gradient. Moreover, the vector field $X$ decomposes as the sum of a Killing vector field $Y$ and the gradient of a suitable function.

math.DG↗

arXiv2012

Characterizations and integral formulae for generalized quasi-Einstein metrics

The aim of this paper is to present some structural equations for generalized quasi-Einstein metrics which was defined recently by Catino in [12]. In addition, supposing that the Riemannian manifold is Einstein we shall show that it is a space form with a well defined potential function f. Finally, we shall derive some integral formulae for such a class of compact manifolds which permit to obtain some rigidity results.

math.DG↗

arXiv2011

Rotational Linear Weingarten Surfaces into the Euclidean Sphere

The aim of this paper is to present a complete description of all rotational linear Weingarten surface into the Euclidean sphere S3. These surfaces are characterized by a linear relation aH+bK=c, where H and K stand for their mean and Gaussian curvatures, respectively, whereas a; b and c are real constants.

math.DG↗