Algebraic, topological and analytical techniques in differential geometry and geometric analysis

• Grant number: 16/23746-6
• Support Opportunities: Research Projects - Thematic Grants
• Start date: July 01, 2017
• End date: June 30, 2023
• 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: Claudio Gorodski ; Francesco Mercuri ; Marcos Martins Alexandrino da Silva ; Ruy Tojeiro de Figueiredo Junior
• Associated researchers: Alexandre Paiva Barreto ; Ana Cláudia da Silva Moreira ; André Salles de Carvalho ; Cristián Andrés Ortiz González ; Dirk Toeben ; Fábio Armando Tal ; Fernando Manfio ; Francisco José Gozzi ; Gaetano Siciliano ; Glaucio Terra ; Guillermo Antonio Lobos Villagra ; Ivan Struchiner ; Llohann Dallagnol Sperança ; Luiz Roberto Hartmann Junior ; Martha Patricia Dussan Angulo ; Patricia Romano Cirilo ; Pedro Paiva Zühlke d'Oliveira
• Associated research grant(s): 23/08567-1 - Pure and Applied Diferential Geometry (PADGE)-2023, AR.EXT; 22/16384-1 - Connections with Prescribed Curvature via Poisson Geometry, AV.EXT; 22/14254-3 - Geometric dynamics between São Paulo and New York, AP.R SPRINT; + associated grants 22/13010-3 - Orthogonal geodesics in manifolds with singular boundary. Applications to the theory of minimal surfaces., AV.EXT; 19/19891-9 - Minimal spheres in ellipsoids, AV.EXT; 19/16286-7 - Topics on curved and flat manifolds, AP.R SPRINT; 19/23370-4 - Symmetry and Shape, AR.EXT; 19/09045-3 - Geometry and dynamics between São Paulo and New York, AP.R SPRINT; 19/12180-0 - Four topics on curved and flat manifolds, AV.EXT; 17/22098-3 - Moduli space of flat metrics, AV.EXT; 17/26597-4 - 20th School of Differential Geometry, AR.BR; 17/22091-9 - Cohomology of Lie algebroids in the holomorphic and algebraic settings: theory and applications, AV.EXT - associated grants
• Associated scholarship(s): 23/04597-3 - Spectral geometry of embeddings and fibre bundles, BP.PD; 22/13818-0 - The Cheeger-Gromoll Splitting Theorem and Applications, BP.MS; 22/16298-8 - Enneper Submanifolds of Constant Sectional Curvature, BP.DR; + associated scholarships 21/10816-4 - Introduction to Riemannian Geometry, BP.IC; 21/03304-7 - Enneper surfaces, BP.MS; 21/05766-8 - Complete surfaces in homogeneous spaces with constant mean curvature, BP.MS; 21/03599-7 - From geometric analysis to bifurcation, BP.PD; 20/13512-3 - A topological and dynamical approach to Fractal Geometry, BP.MS; 21/00551-3 - Finsler distance function and wavefronts, BP.IC; 20/07566-3 - Qualitative properties for higher order and non-local PDEs arising in Differential Geometry, BP.PD; 20/12018-5 - Higher Structures in Geometry and Mathematical Physics, BP.PD; 19/20789-4 - Deformations of geometric structures and Lie groupoids, BP.PD; 20/03431-6 - Uniqueness of immersed spheres in three-dimensional Riemannian manifolds and Enneper-type hypersurfaces, BP.PD; 19/26177-0 - Complete real Kaehler submanifolds, BP.PD; 19/14777-3 - The interplay between Lie groupoids and Riemannian Geometry, BP.PD; 19/16142-5 - Classification of surfaces, BP.IC; 19/19494-0 - Virtual immersions, isometric immersions of product manifolds and conformal genuine rigidity, BP.PD; 19/22488-1 - Some mechanical applications in Riemannian and Finslerian geometry, BP.IC; 19/18940-6 - Geometric applications of the maximum principle, BP.IC; 19/04344-2 - Embedded minimal surfaces in R^3, BP.IC; 19/04027-7 - Submanifolds of codimension two with constant Moebius curvature and flat normal bundle, BP.DR; 18/14980-0 - Geometry and topology of Riemannian foliations via deformations, BP.PD; 17/24680-1 - Metric deformations and applications, BP.DR; 17/22704-0 - Bifurcation in geometric variational problems, BP.DR - associated scholarships

Abstract

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 general relativity; 4) Lusternik-Schnirelman Theory, Morse Theory; 5) geometric variational problems and PDEs on manifolds; 6) isometric immersions in riemannian and pseudo-riemannian manifolds; 7) geometric theory of foliations; 8) Lie groupoids and algebroids, Poisson and Dirac geometry, G-structures; 9) Finsler and pseudo-Finsler manifolds. (AU)

Scientific publications

(37)

(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)

DO REI FILHO, C.; TOJEIRO, R.. Conformally flat hypersurfaces with constant scalar curvature. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 61, p. 133-146, DEC 2018. (16/23746-6)

ALEKSEEVSKY, DMITRI; GORODSKI, CLAUDIO. Semisimple symmetric contact spaces. INDAGATIONES MATHEMATICAE-NEW SERIES, v. 31, n. 6, p. 1110-1133, NOV 2020. (16/23746-6)

BETTIOL, RENATO G.; LAURET, EMILIO A.; PICCIONE, PAOLO. The First Eigenvalue of a Homogeneous CROSS. JOURNAL OF GEOMETRIC ANALYSIS, v. 32, n. 3, MAR 2022. (19/19891-9, 19/09045-3, 16/23746-6)

LOBOS, G. A.; TASSI, M. P.; YUCRA HANCCO, A. J.. Pseudo-parallel surfaces of S-c(n) x R and H-c(n) x R. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 50, n. 3, p. 705-715, SEP 2019. (16/23746-6)

DAJCZER, MARCOS; TOJEIRO, RUY. Hypersurfaces of space forms carrying a totally geodesic foliation. Geometriae Dedicata, v. 205, n. 1, p. 129-146, APR 2020. (16/23746-6)

CANEVARI, S.; TOJEIRO, RUY. Isometric immersions of space forms into S-p x R. Mathematische Nachrichten, v. 293, n. 7, p. 1259-1277, JUL 2020. (16/23746-6)

DE LIMA, R. F.; MANFIO, F.; DOS SANTOS, J. P.. Hypersurfaces of constant higher-order mean curvature in M x R. Annali di Matematica Pura ed Applicata, v. N/A, p. 50-pg., 2022-06-20. (16/23746-6)

LOBOS, G. A.; TASSI, M. P.. A classification of pseudo-parallel hypersurfaces of S-n x R and H-n x R. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 62, p. 72-82, FEB 2019. (16/23746-6)

BEZERRA, A. C.; MANFIO, F.. Rigidity and stability estimates for minimal submanifolds in the hyperbolic space. Journal of Mathematical Analysis and Applications, v. 495, n. 2, MAR 15 2021. (16/23746-6)

CANEVARI, SAMUEL; DE FREITAS, GUILHERME MACHADO; GUIMARAES, FELIPPE; MANFIO, FERNANDO; DOS SANTOS, JOAO PAULO. Complete submanifolds with relative nullity in space forms. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 59, n. 1, p. 81-92, FEB 2021. (19/19494-0, 16/23746-6)

BENCI, VIERI; NARDULLI, STEFANO; PICCIONE, PAOLO; ACEVEDO, LUIS EDUARDO OSORIO. Lusternik-Schnirelman and Morse Theory for the Van der Waals-Cahn-Hilliard equation with volume constraint. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 220, p. 29-pg., 2022-03-18. (16/23746-6, 21/05256-0, 17/13155-3, 18/22938-4)

DUSSAN, M. P.; FRANCO FILHO, A. P.; SANTOS, R. S.. Spacelike minimal surfaces which are graphs in R-1(4). Journal of Mathematical Analysis and Applications, v. 519, n. 2, p. 23-pg., 2023-03-15. (16/23746-6)

BETTIOL, RENATO G.; PICCIONE, PAOLO. Global bifurcation for a class of nonlinear ODEs. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 16, n. 1, p. 22-pg., 2022-02-17. (16/23746-6, 19/09045-3, 19/19891-9)

DE LIMA, R. F.; MANFIO, F.; DOS SANTOS, J. P.. Einstein Hypersurfaces of Warped Product Spaces. Results in Mathematics, v. 77, n. 6, p. 26-pg., 2022-12-01. (16/23746-6)

JIMENEZ, M. I.; TOJEIRO, R.. Infinitesimally Bonnet Bendable Hypersurfaces. JOURNAL OF GEOMETRIC ANALYSIS, v. 33, n. 5, p. 17-pg., 2023-05-01. (16/23746-6)

MANFIO, FERNANDO; TOJEIRO, RUY; VAN DER VEKEN, JOERI. Geometry of submanifolds with respect to ambient vector fields. Annali di Matematica Pura ed Applicata, MAR 2020. (16/23746-6)

CHION, SERGIO; TOJEIRO, RUY. Euclidean Hypersurfaces with Genuine Conformal Deformations in Codimension Two. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, OCT 2019. (16/23746-6)

ALEXANDRINO, MARCOS M.; CARAMELLO JR, FRANCISCO C.. Leaf closures of Riemannian foliations: A survey on topological and geometric aspects of Killing foliations. EXPOSITIONES MATHEMATICAE, v. 40, n. 2, p. 54-pg., 2022-06-01. (18/14980-0, 16/23746-6)

BETTIOL, RENATO G.; LAURET, EMILIO A.; PICCIONE, PAOLO. Full Laplace spectrum of distance spheres in symmetric spaces of rank one. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, v. N/A, p. 22-pg., 2022-04-28. (19/09045-3, 16/23746-6)

JIMENEZ, M. I.; TOJEIRO, R.. Umbilical submanifolds of H-k X Sn-k+1. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 81, p. 19-pg., 2022-04-01. (16/23746-6)

ALEXANDRINO, MARCOS M.; CAVENAGHI, LEONARDO F.; GONCALVES, ICARO. On mean curvature flow of singular Riemannian foliations: Noncompact cases. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 72, p. 18-pg., 2020-10-01. (17/24680-1, 16/23746-6)

CHION, SERGIO; TOJEIRO, RUY. Euclidean Hypersurfaces with Genuine Conformal Deformations in Codimension Two. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 51, n. 3, p. 54-pg., 2019-10-31. (16/23746-6)

MANFIO, FERNANDO; TOJEIRO, RUY; VAN DER VEKEN, JOERI. Geometry of submanifolds with respect to ambient vector fields. Annali di Matematica Pura ed Applicata, v. 199, n. 6, p. 29-pg., 2020-03-03. (16/23746-6)

GORODSKI, CLAUDIO; GUIMARAES, FELIPPE. The κ-nullity of Riemannian manifolds and their splitting tensors. Annali di Matematica Pura ed Applicata, v. 202, n. 6, p. 23-pg., 2023-05-18. (16/23746-6, 19/19494-0)

BETTIOL, RENATO G.; DERDZINSKI, ANDRZEJ; MOSSA, ROBERTO; PICCIONE, PAOLO. Subspace foliations and collapse of closed flat manifolds. Mathematische Nachrichten, v. 295, n. 12, p. 19-pg., 2022-10-31. (19/19891-9, 19/16286-7, 16/23746-6, 18/08971-9)

FREITAS, SIMONE R.; CONSTANTINO, EVERTON; ALEXANDRINO, MARCOS M.. Computational geometry applied to develop new metrics of road and edge effects and their performance to understand the distribution of small mammals in an Atlantic forest landscape. ECOLOGICAL MODELLING, v. 388, p. 24-30, NOV 24 2018. (16/23746-6, 99/05123-4, 01/13309-2)

LIU, ZHISU; SICILIANO, GAETANO. A perturbation approach for the Schrodinger-Born-Infeld system: Solutions in the subcritical and critical case. Journal of Mathematical Analysis and Applications, v. 503, n. 2, NOV 15 2021. (18/17264-4, 19/27491-0, 16/23746-6)

ALEXANDRINO, MARCOS M.; INAGAKI, MARCELO K.; DE MELO, MATEUS; STRUCHINER, IVAN. ie groupoids and semi-local models of singular Riemannian foliation. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 61, n. 3, p. 593-619, APR 2022. (15/22059-2, 19/14777-3, 16/23746-6)

GORODSKI, CLAUDIO. Highly curved orbit spaces. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 63, p. 145-165, APR 2019. (16/23746-6)

ALEXANDRINO, MARCOS M.; ALVES, BENIGNO O.; DEHKORDI, HENGAMEH R.. On Finsler transnormal functions. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 65, p. 93-107, AUG 2019. (16/23746-6)

GORODSKI, CLAUDIO; MENDES, RICARDO A. E.; RADESCHI, MARCO. Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 58, n. 4, AUG 2019. (16/23746-6)

DO REI FILHO, C.; TOJEIRO, R.. Minimal Conformally Flat Hypersurfaces. JOURNAL OF GEOMETRIC ANALYSIS, v. 29, n. 3, p. 2931-2956, JUL 2019. (16/23746-6)

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)

DUSSAN, M. P.; FRANCO FILHO, A. P.; SIMOES, P.. Spacelike Surfaces in L-4 with null mean curvature vector and the nonlinear Riccati partial differential equation. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 207, JUN 2021. (16/23746-6)

LOBOS, GUILLERMO; MELARA, MYNOR; PALMAS, OSCAR. Pseudo-parallel Lorentzian Surfaces in Pseudo-Riemannian Space Forms. Results in Mathematics, v. 78, n. 2, p. 30-pg., 2023-04-01. (16/23746-6)

GOMES, ANDRE MAGALHAES DE SA; GORODSKI, CLAUDIO. REPRESENTATIONS OF LOW COPOLARITY. Proceedings of the American Mathematical Society, v. 150, n. 12, p. 9-pg., 2022-12-01. (16/23746-6)

DUSSAN, M. P.; FRANCO FILHO, A. P.; MAGID, M.. Timelike surfaces in the de Sitter space S-1(3) (1) subset of R-1(4). ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 61, n. 4, p. 20-pg., 2022-03-25. (16/23746-6)