Geometry and Topology of Riemannian Manifolds

• Grant number: 99/02684-5
• Support Opportunities: Research Projects - Thematic Grants
• Duration: August 01, 1999 - 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 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)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BRITO, FABIANO G. B.; CHACON, PABLO M.. ENERGY OF GLOBAL FRAMES. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, v. 84, n. 2, p. 155-162, APR 2008. (99/02684-5)

BRITO, FABIANO G. B.; CHACON, PABLO M.; JOHNSON, DAVID L.. UNIT VECTOR FIELDS ON ANTIPODALLY PUNCTURED SPHERES: BIG INDEX, BIG VOLUME. BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, v. 136, n. 1, p. 147-157, 2008. (99/02684-5)

BRITO‚ F.G.B.; CHACÓN‚ P.M.. A topological minorization for the volume of vector fields on 5-manifolds. ARCHIV DER MATHEMATIK, v. 85, n. 3, p. 283-292, 2005. (99/02684-5)

BRITO‚ F.; JOHNSON‚ D.L.. Volume-minimizing foliations on spheres. Geometriae Dedicata, v. 109, n. 1, p. 253-267, 2004. (99/02684-5)

BRITO‚ F.B.; CHACÓN‚ P.M.; NAVEIRA‚ AM. On the volume of unit vector fields on spaces of constant sectional curvature. COMMENTARII MATHEMATICI HELVETICI, v. 79, n. 2, p. 300-316, 2004. (99/02684-5)