CV Lattes
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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Obtained his master degree in Mathematics at the Universidade Federal de Minas Gerais (1982) and his PhD at the Instituto de Matemática Pura e Aplicada (1991). His research are is Differential Geometry, with emphasis on Submanifold theory. His current research interests include: transformations of submanifolds, isometric and conformal deformations of submanifolds and Moebius geometry. (Source: Lattes Curriculum)
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The researchers and students participating in this project to investigate new trends regarding differential geometric methods used in modern theories of Mathematics and Physics. The project program combines research in differential geometry and geometric analysis. Transcending the boundaries of the associated subprojects are a range of modern techniques such as geometric flows, PDE soluti…
The projets addresses several topics in differential geometry and geometric analysis, including: 1) group and groupoid actions in riemannian and pseudo-riemannian manifolds; 2) submanifold theory, minimal submanifolds and constant mean curvature hypersurfaces; 3) variational calculus and global analysis in riemannian, sub-riemannian and pseudo-riemannian geometry, with applications to gen…
The project deals with some central topics in Riemannian and pseudo-Riemannian Geometry, such as: (1) submanifold theory, (2) isometric actions, (3) minimal and constant mean curvature immersions, (4) geometric variational problems. (AU)
The project involves classical problems in submanifold geometry of local and global character, namely, isometric, affine, minimal, umbilical, conformal and isoparametric immersions in several ambient spaces of finite and infinite dimension, as well as the existence problem for closed geodesics in Riemannian and pseudo-Riemannian manifolds. The methods of investigation involve Lie group ac…
(Only some records are available in English at this moment)
This project belongs to the field of Differential Geometry, in the subarea of Submanifold Theory. More precisely, we are interested in the isometric rigidity problem.
In this project, we intend to study holonomic submanifolds with flat normal bundle whose lines of curvature are contained in planes or spheres called Enneper submanifolds aiming the constant curvature ones.
This project lies in the domain of Differential Geometry. The main objective is to study geometric aspects of submanifolds in Riemannian manifolds. More precisely, we are interested in the following topics: isometric, conformal and infinitesimal rigidity aspects of submanifolds of the Euclidean space and other ambient spaces. (AU)
This proposal pretends to interlace tools from singularity theory and differential geometry in thestudy of frontals in high co-dimension, mainly focused in minimal surfaces with singular points and branched immersions in high dimensions, generalizing tools of my thesis.In my doctoral thesis, we introduce tools to investigate the differential geometry of singular surfaces known as frontals…
An umbilic-free surface in Euclidean space R^3 whose curvature lines correspondent to one of its principal curvatures are contained in spheres or planes is called an Enneper surface. In this project we present a parametrization of Enneper surfaces with one family of planar curvature lines in terms of Ribaucour partial tubes, introduced in recent work by S. Chión and R. Tojeiro, and descri…
Part of our project consists in the study of general hypotheses on a certain class of surfaces in order to guarantee uniqueness of spheres immersed in three-dimensional Riemannian manifolds, in the sense of the generalized version of Hopf's Theorem proved by J.A. Gálvez and P. Mira (Uniqueness of immersed spheres in three-manifolds, to appear in Journal of Differential Geometry). We also …
(Only some records are available in English at this moment)
This project corresponds to a BEPE proposal associated to the postdoctoral scholarship of FAPESP with process number 2024/03493-2. The subject of this project lies in the domain of Differential Geometry, mainly with the subarea of Geometric Analysis. To be more precise, we will study a slightly modified notion of a Zoll family of minimal hypersurfaces. This new notion has the benefit that…
This research project investigates a generalization of Joachimsthal surfaces in higher dimensions and codimensions, specifically targeting those with constant sectional curvature. By generalizing Joachimsthal surfaces, we also aim to address whether Enneper surfaces in higher dimensions with nonzero constant sectional curvature necessarily fall within this subclass, which is known to be t…
The subject of this project lies in the domain of Differential Geometry, it deals with a notion of deformation of submanifolds. More specifically, it deals with variations of submanifolds that are infinitesimal with respect to the metric and the mean curvature. (AU)
The aim of this project is to investigate Joachimsthal hypersurfaces in R3 with relevant geometric properties, such as constant Gaussian or constant mean curvatures, Weingarten surfaces, etc., in the light of the explicit description of such hypersurfaces in terms of certain differentiable functions of one variable and certain curves in the hyperbolic plane whose coordinate functions sati…
| 1 / 1 | Ongoing grants |
| 6 / 5 | Completed research grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 8 / 5 | Completed scholarships in Brazil |
| 2 / 2 | Ongoing scholarships abroad |
| 2 / 2 | Completed scholarships abroad |
| 22 / 18 | All research grants and scholarships |
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