arXiv subjects

Ícaro Gonçalves

Publications and source records attributed to Ícaro Gonçalves.

3 recordsLinked to original sources

arXiv2024

Foliations transverse to a closed conformal vector field

In this article, we study the geometric properties of codimension one foliations on Riemannian manifolds equipped with vector fields that are closed and conformal. Apart from its singularities, these vector fields define codimension one foliations with nice geometric features, which we call Montiel Foliations. We investigate conditions for which a foliation transverse to this structure has totally geodesic leaves, as well as how the ambient space and the geometry of the leaves forces a given foliation into a Montiel Foliation. Our main results concern minimal leaves and constant mean curvature foliations, having compact or complete noncompact leaves. Finally, we characterize totally geodesic foliations by means of its relation to a prior Montiel Foliation.

math.DG↗

arXiv2020

Area minimizing unit vector fields on antipodally punctured unit 2-sphere and minimally immersed Klein Bottles

We provide a lower value for the volume of a unit vector field tangent to an antipodally Euclidean sphere $\mathbb{S}^2$ depending on the length of an ellipse determined by the indexes of its singularities. In addition, for minimizing vector fields having specific pair of indexes, we show that their image coincides with the image of minimally immersed Klein bottles.

math.DG↗

arXiv2017

Topological invariants for closed hypersurfaces

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 allows us to obtain topological invariants for the immersion that depends on the geometry of the manifold and the ambient space. We use these quantities to find obstructions to the existence of certain codimension one foliations.

math.DG↗