| Grant number: | 99/02684-5 |
| Support Opportunities: | Research Projects - Thematic Grants |
| Start date: | August 01, 1999 |
| End date: | September 30, 2004 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal Investigator: | Fabiano Gustavo Braga Brito |
| Grantee: | Fabiano Gustavo Braga Brito |
| Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| Pesquisadores principais: | Alcibiades Rigas ; Antonio Carlos Asperti ; Francesco Mercuri |
| Associated research grant(s): | 04/01059-0 - Juan Carlos Alvarez-Paiva | Polytechnic University - Estados Unidos,
AV.EXT 02/10725-8 - Maria Helena Noronha | California State University Northridge - Estados Unidos, AV.EXT |
Abstract
A central theme in Differential Geometry is the study of relations between pointwise invariants (Linear Algebra), local invariant (Analysis) and global invariants (Topology) of a Riemannian manifold. This study is done, in general, for certain classes of Riemannian manifolds. Our research is concerned manely with the following ones: - Submanifolds of a space of constant curvature with prescribed conditions on the codimension, second fundamental form, curvatures, etc. - Lie groups, symmetric spaces and, in general, principal bundles: We study the existence of special metrics, geometric realization of topological invariants as homotopy classes and special submanifolds. - Submanifolds associated to minimizers of geometric variational problems, envolving functionals like volume, energy, isoperimetric quotient, associated to maps between manifolds. (AU)
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