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    A lower bound for the norm of the second fundamental form of minimal hypersurfaces of \( \mathbb{S}^{n+1} \)

    The aim of this paper is to give an estimate for the squared norm S of the second fundamental form A of a compact minimal hypersurface ...

    J. N. Barbosa, A. Barros in Archiv der Mathematik (2003)

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    Estimate for index of hypersurfaces in spheres with null higher order mean curvature

    In a recent paper (Barros, Sousa in: Kodai Math. J. 2009) the authors proved that closed oriented non-totally geodesic minimal hypersurfaces of the Euclidean unit sphere have index of stability greater than or...

    A. Barros, P. Sousa in Monatshefte für Mathematik (2010)

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    Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons

    The aim of this paper is to present a link between the Perelman potential for a compact Ricci soliton M n and the Hodge-de Rham decomposition theorem, we shall ...

    C. Aquino, A. Barros, E. Ribeiro Jr. in Results in Mathematics (2011)

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    Rotational linear Weingarten surfaces into the Euclidean sphere

    The aim of this paper is to present a complete description of all rotational linear Weingarten surfaces in the Euclidean sphere $$\mat...

    A. Barros, J. Silva, P. Sousa in Israel Journal of Mathematics (2012)

  5. Article

    Erratum to: Some Applications of the Hodge-de Rham Decomposition to Ricci solitons

    The aim of this note is to clarify a minor mistake in the article: Some Applications of the Hodge-de Rham Decomposition to Ricci solitons.

    C. Aquino, A. Barros, E. Ribeiro Jr. in Results in Mathematics (2013)

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    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 \(\big (M^n,\,g,\,X,\,\lambda \big )\) ...

    A. Barros, R. Batista, E. Ribeiro Jr. in Monatshefte für Mathematik (2014)

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    Bach-Flat Critical Metrics of the Volume Functional on 4-Dimensional Manifolds with Boundary

    The purpose of this article is to investigate Bach-flat critical metrics of the volume functional on a compact manifold \(M\) ...

    A. Barros, R. Diógenes, E. Ribeiro Jr. in The Journal of Geometric Analysis (2015)

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    On locally conformally flat critical metrics for quadratic functionals

    The aim of this note is to present some results about critical metrics for quadratic functional \({\mathcal {F}}_{t,s}\) ...

    A. Barros, A. Da Silva in Annals of Global Analysis and Geometry (2017)

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    On static manifolds and related critical spaces with zero radial Weyl curvature

    The aim of this paper is to study compact Riemannian manifolds \((M,\,g)\)(M,g) that admit a non-constant solution to the system of equations $$\begin{aligned} -\Delta f\, g+Hess f-fRic=\mu Ric+\lambda g, \end{al...

    H. Baltazar, A. Barros, R. Batista, E. Viana in Monatshefte für Mathematik (2020)

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    Free Boundary Hypersurfaces with Non-positive Yamabe Invariant in Mean Convex Manifolds

    We obtain some estimates on the area of the boundary and on the volume of a certain free boundary hypersurface \(\Sigma \) Σ with non-positive Yamabe invariant in a Riemannian n-manifold with bounds for the s...

    A. Barros, C. Cruz in The Journal of Geometric Analysis (2020)