Group actions, submanifold theory and global analysis in Riemannian and pseudo-Riemannian geometry

• Grant number: 11/21362-2
• Support Opportunities: Research Projects - Thematic Grants
• Duration: April 01, 2012 - April 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paolo Piccione
• Grantee: Paolo Piccione
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Pesquisadores principais:( Últimos ): Claudio Gorodski ; Francesco Mercuri ; Marcos Martins Alexandrino da Silva ; Ruy Tojeiro de Figueiredo Junior
• Pesquisadores principais:( Antigos ): Henri Nicolas Guillaume Anciaux
• Associated researchers: Claudemir Silvino Leandro ; Cristián Andrés Ortiz González ; Dirk Toeben ; Fernando Manfio ; Gaetano Siciliano ; Guillermo Antonio Lobos Villagra ; Henri Nicolas Guillaume Anciaux ; Henrique de Barros Correia Vitorio ; Ivan Struchiner ; Martha Patricia Dussan Angulo ; Ricardo Gallego Torrome ; Sinue Dayan Barbero Lodovici
• Associated grant(s): 16/22104-0 - Topics in the theory of minimal isometric immersions, AV.BR; 17/00639-2 - VII Workshop on Differential Geometry, AR.BR; 15/50470-9 - Geometric analysis and variational problems in Riemannian and Kähler geometry, AP.R SPRINT; + associated grants 15/01997-4 - A non-archimedean approach to the Riemannian isoperimetric problem, AV.EXT; 14/50150-1 - Geometry in London and São Paulo, AP.R; 13/21070-7 - Geometry of quadratic Finsler metrics, AV.EXT; 13/50325-3 - Geometry in Columbus and São Paulo, AP.R; 13/10451-0 - Mean curvature esitimates for submanifolds, AV.BR; 13/04097-9 - Polar symplectic representations, AV.EXT; 12/09925-4 - Geometric invariants in Differentiable manifolds, AV.BR; 12/15970-2 - Conference on Pure and Applied Differential Geometry, AR.EXT - associated grants
• Associated scholarship(s): 16/24515-8 - The Morse index for minimal surfaces into the sphere S^3, BP.IC; 15/19850-0 - Real analysis, BP.IC; 14/25190-0 - Kahlerian methods in Riemannian Geometry, BP.PD; + associated scholarships 14/22568-1 - Proper actions and foliations in Riemannian geometry, BP.PD; 14/22556-3 - Geometry of isoparametric submanifolds of Hilbert space and topology of spaces of curves with bounded curvature on surfaces., BP.PD; 14/01989-9 - Generalized Willmore surfaces, BE.PQ; 14/04517-0 - Topics of bifurcation theory in geometric variational problems, BP.DD; 12/22490-7 - Topics in Geometric Analysis in Riemannian Manifolds, BP.PD; 12/11950-7 - Topics in Mathematical Relativity, BP.PD - associated scholarships

Abstract

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)

Scientific publications

(26)

(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)

PISANI, LORENZO; SICILIANO, GAETANO. CONSTRAINED SCHRODINGER-POISSON SYSTEM WITH NON-CONSTANT INTERACTION. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, v. 15, n. 1, FEB 2013. (11/21362-2, 11/01081-9)

GORODSKI, CLAUDIO; LYTCHAK, ALEXANDER. The curvature of orbit spaces. Geometriae Dedicata, v. 190, n. 1, p. 135-142, OCT 2017. (11/21362-2)

ANCIAUX, HENRI; PANAGIOTIDOU, KONSTANTINA. Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 42, p. 1-14, OCT 2015. (11/21362-2)

DAJCZER, MARCOS; TOJEIRO, RUY. SUBMANIFOLDS WITH NONPARALLEL FIRST NORMAL BUNDLE REVISITED. PUBLICACIONS MATEMATIQUES, v. 58, n. 1, p. 179-191, 2014. (11/21362-2)

TOJEIRO, RUY. A DECOMPOSITION THEOREM FOR IMMERSIONS OF PRODUCT MANIFOLDS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 59, n. 1, p. 247-269, FEB 2016. (11/21362-2)

GORODSKI, CLAUDIO; KOLLROSS, ANDREAS. Some remarks on polar actions. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 49, n. 1, p. 43-58, JAN 2016. (11/21362-2)

GORODSKI, CLAUDIO; PODESTA, FABIO. Tight Lagrangian homology spheres in compact homogeneous Kahler manifolds. Israel Journal of Mathematics, v. 206, n. 1, p. 413-429, FEB 2015. (11/21362-2)

GORODSKI, CLAUDIO; LYTCHAK, ALEXANDER. Isometric actions on spheres with an orbifold quotient. MATHEMATISCHE ANNALEN, v. 365, n. 3-4, p. 1041-1067, AUG 2016. (11/21362-2)

ORJUELA, JAIME; TOJEIRO, RUY. UMBILICAL SURFACES OF PRODUCTS OF SPACE FORMS. TOHOKU MATHEMATICAL JOURNAL, v. 68, n. 3, p. 471-486, SEP 2016. (11/21362-2)

BETTIOL, RENATO G.; PICCIONE, PAOLO. MULTIPLICITY OF SOLUTIONS TO THE YAMABE PROBLEM ON COLLAPSING RIEMANNIAN SUBMERSIONS. PACIFIC JOURNAL OF MATHEMATICS, v. 266, n. 1, p. 1-21, NOV 2013. (11/21362-2)

DOMINGUEZ-VAZQUEZ, MIGUEL; GORODSKI, CLAUDIO. POLAR FOLIATIONS ON QUATERNIONIC PROJECTIVE SPACES. TOHOKU MATHEMATICAL JOURNAL, v. 70, n. 3, p. 353-375, 2018. (11/21362-2)

D'AVENIA, PIETRO; PISANI, LORENZO; SICILIANO, GAETANO. Nonautonomous Klein-Gordon-Maxwell systems in a bounded domain. ADVANCES IN NONLINEAR ANALYSIS, v. 3, p. 9-pg., 2014-09-01. (11/21362-2)

BETTIOL, RENATO G.; PICCIONE, PAOLO; SICILIANO, GAETANO. ON THE EQUIVARIANT IMPLICIT FUNCTION THEOREM WITH LOW REGULARITY AND APPLICATIONS TO GEOMETRIC VARIATIONAL PROBLEMS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 58, n. 1, p. 53-80, FEB 2015. (10/00068-6, 11/21362-2)

GORODSKI, CLAUDIO; LYTCHAK, ALEXANDER. REPRESENTATIONS WHOSE MINIMAL REDUCTION HAS A TORIC IDENTITY COMPONENT. Proceedings of the American Mathematical Society, v. 143, n. 1, p. 379-386, JAN 2015. (11/21362-2)

ANCIAUX, HENRI; ROMON, PASCAL. A canonical structure on the tangent bundle of a pseudo- or para-Kahler manifold. MONATSHEFTE FUR MATHEMATIK, v. 174, n. 3, p. 329-355, JUL 2014. (11/21362-2)

ANCIAUX, HENRI; CIPRIANI, NASTASSJA. Codimension two marginally trapped submanifolds in Robertson-Walker spacetimes. JOURNAL OF GEOMETRY AND PHYSICS, v. 88, p. 105-112, FEB 2015. (11/21362-2)

MENDONCA, BRUNO; TOJEIRO, RUY. Umbilical Submanifolds of S-n x R. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, v. 66, n. 2, p. 400-428, APR 2014. (11/21362-2)

ANCIAUX, HENRI. MARGINALLY TRAPPED SUBMANIFOLDS IN SPACE FORMS WITH ARBITRARY SIGNATURE. PACIFIC JOURNAL OF MATHEMATICS, v. 272, n. 2, p. 257-274, DEC 2014. (11/21362-2)

CANEVARI, S.; TOJEIRO, R.. Hypersurfaces of two space forms and conformally flat hypersurfaces. Annali di Matematica Pura ed Applicata, v. 197, n. 1, p. 1-20, FEB 2018. (11/21362-2)

GORODSKI, CLAUDIO; RADESCHI, MARCO. On homogeneous composed Clifford foliations. MUENSTER JOURNAL OF MATHEMATICS, v. 9, n. 1, p. 35-50, 2016. (11/21362-2)

D'AVENIA, PIETRO; PISANI, LORENZO; SICILIANO, GAETANO. Nonautonomous Klein-Gordon-Maxwell systems in a bounded domain. ADVANCES IN NONLINEAR ANALYSIS, v. 3, n. 1, p. S37-S45, SEP 2014. (11/21362-2)

GORODSKI, CLAUDIO; SATURNINO, ARTUR B.. Focal radii of orbits. LINEAR & MULTILINEAR ALGEBRA, v. 67, n. 10, p. 2082-2103, OCT 3 2019. (11/21362-2)

ALEXANDRINO, MARCOS M.; ALVES, BENIGNO O.; ANGEL JAVALOYES, MIGUEL. On singular Finsler foliation. Annali di Matematica Pura ed Applicata, v. 198, n. 1, p. 205-226, FEB 2019. (16/23746-6, 11/21362-2)

GEATTI, LAURA; GORODSKI, CLAUDIO. Polar Symplectic Representations. ALGEBRAS AND REPRESENTATION THEORY, v. 20, n. 3, p. 751-764, JUN 2017. (11/21362-2)

ANCIAUX, HENRI. Surfaces with one constant principal curvature in three-dimensional space forms. BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, v. 56, n. 2, p. 641-653, OCT 2015. (11/21362-2)

GORODSKI, CLAUDIO; GOZZI, FRANCISCO J.. Representations with Sp(1)(k)-reductions and quaternion-Kahler symmetric spaces. MATHEMATISCHE ZEITSCHRIFT, v. 290, n. 1-2, p. 561-575, OCT 2018. (14/22568-1, 11/21362-2)