Isometric immersions of (intrinsically) homogeneous manifolds

• Grant number: 21/12348-8
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: March 01, 2022
• End date: October 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Gorodski
• Grantee: Felippe Soares Guimarães
• Supervisor: Joeri Van der Veken
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of Leuven, 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: When isometric immersions of (intrinsically) homogeneous manifolds in space forms in low codimension 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 techniques about isometric rigidity to study Riemannian manifolds in dimensions greater than 2. This project also aims to study homogeneous hypersurfaces in complex space forms and products of space forms, with the same objective, to determine when such hypersurfaces are extrinsically homogeneous. Although there are not so many results about isometric rigidity in the literature for these ambient spaces, the author intends to obtain results about isometric rigid similar to the classical ones adapted to this problem, that is, for isometric immersions that come from intrinsic rigid movements. (AU)