Felippe Guimarães

activity

20152026

collaborators

10 papers

math.DG2026

Congruence theorems for capillary hypersurfaces and a substatic Heintze--Karcher inequality

Felippe Guimarães

We prove congruence theorems for capillary hypersurfaces of Euclidean space supported on a hyperplane or on a sphere, extending a result of Ros for closed hypersurfaces. We also es…

math.DG2024

On minimal homogeneous submanifolds of the hyperbolic space up to codimension two

Felippe Guimarães, Joeri Van der Veken

We show that a minimal homogeneous submanifold $M^{n}$ , $n \geq 5$ , of a hyperbolic space up to codimension two is totally geodesic.

math.DG2023

A note on parallel mean curvature surfaces and Codazzi operators

Felippe Guimarães

We present an intrinsic Klotz-Osserman type theorem for surfaces in terms of Codazzi operators. Additionally, utilizing Simons' formula, we investigate surfaces with parallel mean…

math.DG2022

Isoparametric hypersurfaces of Riemannian manifolds as initial data for the mean curvature flow

Felippe Guimarães, João Batista Marques dos Santos, João Paulo dos Santos

We show that the evolution of isoparametric hypersurfaces of Riemannian manifolds by the mean curvature flow is given by a reparametrization of the parallel family in short time, a…

math.DG2022

Generalized warped products and the $κ$ -nullity of Riemannian curvature

Claudio Gorodski, Felippe Guimarães

In this short survey, we show how two (classes of) known examples of inhomogeneous, curvature homogeneous Riemannian manifolds with nontrivial $κ$ -nullity can be seen as deformatio…

math.DG2019

Complete submanifolds with relative nullity in space forms

Samuel Canevari, Guilherme Machado de Freitas, Felippe Guimarães +2

We use techniques based on the splitting tensor to explicitly integrate the Codazzi equation along the relative nullity distribution and express the second fundamental form in term…

math.DG2019

Real Kähler Submanifolds in Codimension $6$

Alcides de Carvalho, Felippe Guimarães

We show that a real Kähler submanifold in codimension $6$ is essentially a holomorphic submanifold of another real Kähler submanifold in lower codimension if the second fundamental…

math.DG2018

Conformal immersion of Riemannian products in low codimension

Felippe Guimarães, Bruno Mendonça

We proved that a conformal immersion of $M_{0}^{n_{0}} \times M_{1}^{n_{1}}$ as an hipersurface in a Euclidean space must be an extrinsic product of immersions, under the assumption that $n…

math.DG2018

Singular genuine rigidity

Luis A. Florit, Felippe Guimarães

We extend the concept of genuine rigidity of submanifolds by allowing mild singularities, mainly to obtain new global rigidity results and unify the known ones. As one of the conse…

math.DG2015

Cylindricity of complete Euclidean submanifolds with relative nullity

Felippe Soares GuimarÃes, Guilherme Machado De Freitas

We show that a complete Euclidean submanifold with minimal index of relative nullity $ν_{0} > 0$ and Ricci curvature with a certain controlled decay must be a $ν_{0}$ -cylinder. This is a…

Congruence theorems for capillary hypersurfaces and a substatic Heintze--Karcher inequality

On minimal homogeneous submanifolds of the hyperbolic space up to codimension two

A note on parallel mean curvature surfaces and Codazzi operators

Isoparametric hypersurfaces of Riemannian manifolds as initial data for the mean curvature flow

Generalized warped products and the κ-nullity of Riemannian curvature

Complete submanifolds with relative nullity in space forms

Real Kähler Submanifolds in Codimension 6

Conformal immersion of Riemannian products in low codimension

Singular genuine rigidity

Cylindricity of complete Euclidean submanifolds with relative nullity

Generalized warped products and the $κ$ -nullity of Riemannian curvature

Real Kähler Submanifolds in Codimension $6$