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Isometric immersions of (intrinsically) homogeneous manifolds

Grant number: 21/12348-8
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): March 01, 2022
Effective date (End): October 31, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Claudio Gorodski
Grantee:Felippe Soares Guimarães
Supervisor abroad: Joeri Van Der Veken
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Research place: University of Leuven (KU Leuven), Belgium  
Associated to the scholarship:19/19494-0 - Virtual immersions, isometric immersions of product manifolds and conformal genuine rigidity, BP.PD

Abstract

This project is built around the following central research question: Whenisometric immersions of (intrinsically) homogeneous manifolds in space forms in lowcodimension are orbits of a subgroup of the isometries of the ambient space, that is,extrinsically homogeneous. More precisely, this project aims to apply the recently developed techniquesabout isometric rigidity to study Riemannian manifolds in dimensionsgreater than 2. This project also aims to study homogeneous hypersurfaces in complex space formsand products of space forms, with the same objective, to determine when suchhypersurfaces are extrinsically homogeneous. Although there are not so many resultsabout isometric rigidity in the literature for these ambient spaces, the author intendsto obtain results about isometric rigid similar to the classical ones adapted to this problem, that is, for isometricimmersions that come from intrinsic rigid movements.

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