4 papers
Spherical 2-Dupin submanifolds
Antonio J. Di Scala, Guilherme Machado de Freitas
We show that every spherical 2-Dupin submanifold that is not a hypersurface is conformally congruent to the standard embedding of the real, complex, quaternionic or octonionic proj…
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 and Ricci curvature with a certain controlled decay must be a -cylinder. This is a…
Classification of codimension two deformations of rank two Riemannian manifolds
Luis A. Florit, Guilherme M. de Freitas
The purpose of this work is to close the local deformation problem of rank two Euclidean submanifolds in codimension two by describing their moduli space of deformations. In the pr…
Submanifolds With Homothetic Gauss Map In Codimension Two
Guilherme Machado de Freitas
In this article we derive a complete classification of all submanifolds in space forms with codimension two for which the Gauss map is homothetic.