1 citations · 1 across the 4 of their papers we have counts for
7 papers
Zoll manifolds with boundary
Eduardo Longa, Paolo Piccione, Roney Santos
We introduce and study Zoll manifolds with boundary: compact Riemannian manifolds with smooth boundary such that every geodesic issuing orthogonally from the boundary returns ortho…
Extremal metrics for the eigenvalues of the Laplacian on manifolds with boundary
Eduardo Longa
We show there are no extremal metrics for the eigenvalues of the Neumann Laplacian on any compact manifold. Nonetheless, we construct examples of conformally extremal metrics for t…
Sharp systolic inequalities for -manifolds with boundary
Eduardo Longa
We prove some sharp systolic inequalities for compact -manifolds with boundary. They relate the (relative) homological systoles of the manifold to its scalar curvature and mean…
Topological rigidity for closed hypersurfaces of elliptic space forms
Eduardo Longa, Jaime Ripoll
We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absol…
Gauss map and the topology of constant mean curvature hypersurfaces of and
Fidelis Bittencourt, Pedro Fusieger, Eduardo Longa +1
We define a Gauss map of an oriented hypersurface of the unit sphere and prove that is harmonic if and only if has CMC.…
Topological invariants for closed hypersurfaces
Ícaro Gonçalves, Eduardo Longa
We consider closed and orientable immersed hypersurfaces of translational manifolds. Given a vector field on such a hypersurface, we define a perturbation of its Gauss map, which a…
The Gauss map on translational Riemannian manifolds and the topology of hypersurfaces
Eduardo R. Longa, Jaime B. Ripoll
We introduce the notion of translational Riemannian manifolds and define a Gauss map for orientable immersed hypersurfaces lying in these ambients, an associated translational curv…