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Two integrability problems in the theory of involutive structures

Grant number: 19/27084-6
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): April 01, 2021
Effective date (End): March 31, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Paulo Leandro Dattori da Silva
Grantee:Gabriel Cueva Candido Soares de Araújo
Supervisor abroad: Gerardo A. Mendoza
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Local de pesquisa : Temple University, United States  
Associated to the scholarship:18/12273-5 - Solvability of locally integrable structures, BP.PD

Abstract

We propose to investigate two problems of integrability of involutive structures. The first one, of a global and geometric nature, deals with embeddability of certain classes of compact CR manifolds into model compact complex manifolds (e.g. complex projective spaces), which can be regarded as a global version of a classical local question in CR geometry. The second one, of a more local and analytic flavor, asks for suitable generalizations of the Newlander-Nirenberg Theorem in the framework of manifolds with boundary i.e. for the so-called (almost) complex b-structures. (AU)