Topics in the theory of minimal isometric immersions

• Grant number: 16/22104-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: April 04, 2017
• End date: April 03, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paolo Piccione
• Grantee: Paolo Piccione
• Visiting researcher: Marcos Dajczer
• Visiting researcher institution: Ministério da Ciência, Tecnologia e Inovação (Brasil). Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). Instituto Nacional de Matemática Pura e Aplicada (IMPA), Brazil
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 11/21362-2 - Group actions, submanifold theory and global analysis in Riemannian and pseudo-Riemannian geometry, AP.TEM

Abstract

The projects deals with minimal submanifolds in Euclidean spaces and in spheres. More specifically, we plan to discover new methods of constructing examples of such submanifolds that satisfy additional properties, such as the existence of minimal isometric deformations. In particular, we plan to give explicit constructions of compact, or Kaehler, minimal submanifolds is spheres, as well as associated families of such isometric deformations. (AU)