Submanifold geometry and Morse theory in finite and infinite dimensions

• Grant number: 07/03192-7
• Support Opportunities: Research Projects - Thematic Grants
• Duration: November 01, 2007 - October 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Gorodski
• Grantee: Claudio Gorodski
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Pesquisadores principais: Francesco Mercuri ; Paolo Piccione ; Ruy Tojeiro de Figueiredo Junior
• Associated researchers: Marcos Martins Alexandrino da Silva
• Associated grant(s): 11/01081-9 - Geometric variational problems and PDEs, AV.EXT; 10/00082-9 - Geometry of compact stationary manifolds, AV.EXT; 10/00067-0 - Generic properties and spectral theory for the Laplacian in Lorentzian and Finslerian geometry, AV.EXT
• Associated scholarship(s): 11/12565-7 - Topics in Lorentzian and Finsler Geometry: geodesic flow and isometry group, BP.DR; 10/15502-3 - Geometric variational problems, BP.PD; 10/11934-6 - GLOBAL ASPECTS IN FINSLER AND LORENTZIAN GEOMETRY, BP.PD; + associated scholarships 10/11808-0 - Geometrial and analytical aspects of constant mean curvature immersions, BP.PD; 10/12082-3 - Spectral geometry on singular spaces, BP.PD; 10/02525-5 - Complex Differential Geometry, BP.MS; 10/00068-6 - Variational and topologucal methods for field equations, BP.PD; 08/07604-0 - Generic properties of semi-Riemannian geodesic flows, BP.MS; 08/07368-5 - Dependence of best Riemannian constants in spaces of metrics, BP.PD; 08/04470-3 - Algebraic Curves and Riemann Surfaces, BP.IC; 07/08513-6 - Closed minimal hypersurfaces in noncompact symmetric spaces, BP.DR; 08/01034-8 - Topics in Differential and Riemannian Geometry, BP.IC - associated scholarships

Abstract

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 actions and Morse theory. (AU)

Scientific publications

(4)

(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)

DAJCZER, M.; FLORIT, L.; TOJEIRO, R.. Euclidean hypersurfaces with genuine deformations in codimension two. MANUSCRIPTA MATHEMATICA, v. 140, n. 3-4, p. 621-643, MAR 2013. (07/03192-7)

GORODSKI, CLAUDIO; HEINTZE, ERNST. Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space. Journal of Fixed Point Theory and Applications, v. 11, n. 1, p. 93-136, MAR 2012. (07/03192-7)

ALIAS, L. J.; BESSA, G. P.; MONTENEGRO, J. F.; PICCIONE, P.. Curvature Estimates for Submanifolds in Warped Products. Results in Mathematics, v. 60, n. 1-4, p. 265-286, OCT 2011. (07/03192-7)

GORODSKI, CLAUDIO; LYTCHAK, ALEXANDER. On orbit spaces of representations of compact Lie groups. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, v. 691, p. 61-100, JUN 2014. (07/03192-7)