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Integral Identities and Rigidity of Generalized -Quasi-Einstein Manifolds
Alcides de Carvalho, W. O. Costa-Filho
We prove that every closed -quasi-Einstein manifold with constant is trivial whenever . This establishes the Colling--Dunajski conjecture in the…
On Generalized Quasi-Einstein Manifolds
Alcides de Carvalho, Anderson Lima, W. O. Costa-Filho
In this paper, we study generalized -quasi-Einstein under natural conditions on the potential vector field. We show that, under suitable integral assumptions, the…
Index estimates for harmonic Gauss maps
Alcides de Carvalho, Marcos P. Cavalcante, Wagner Costa-Filho +1
Let denote a closed surface with constant mean curvature in , a 3-dimensional Lie group equipped with a bi-invariant metric. For such surfaces, there is a harmoni…
Remarks on biharmonic hypersurfaces in space forms
Wagner Oliveira Costa-Filho
We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integr…
The r-mean curvature and rigidity of compact hypersurfaces in the Euclidean space
Wagner Oliveira Costa-Filho
In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.
The halfspace theorem for minimal hypersurfaces in regions bounded by minimal cones
Marcos Petrúcio Cavalcante, Wagner Oliveira Costa-Filho
We prove that there are no minimal hypersurfaces properly immersed in any region of the Euclidean space bounded by unstable minimal cones. We also prove the analogous result for $r…