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Virtual immersions, isometric immersions of product manifolds and conformal genuine rigidity

Grant number: 19/19494-0
Support Opportunities:Scholarships in Brazil - Post-Doctorate
Effective date (Start): November 01, 2019
Effective date (End): February 28, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Claudio Gorodski
Grantee:Felippe Soares Guimarães
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis, AP.TEM
Associated scholarship(s):21/12348-8 - Isometric immersions of (intrinsically) homogeneous manifolds, BE.EP.PD


The research topics are in Differential Geometry and involve three subjects: the concept of virtual immersions, which generalizes isometric immersions, with the goal of obtaining structural results for manifolds admitting virtual immersion with nonsymmetric second fundamental form; the study of isometric immersions of product manifolds in low codimension, namely, the use modern tools to attack Moore's conjecture from 1972; and investigate global results related to the recent concept of conformal genuine rigidity, that is, extend Sacksteder's theorem about isometric rigidity to the conformal setting.

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Scientific publications
(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)
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, . (19/19494-0, 16/23746-6)

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