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Article
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 ...
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Article
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...
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Article
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 ...
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Article
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...
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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.
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Article
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 \(\big (M^n,\,g,\,X,\,\lambda \big )\) ...
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Article
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 \(M\) ...
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Article
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 \({\mathcal {F}}_{t,s}\) ...
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Article
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...
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Article
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...