Metric deformations and applications

• Grant number: 17/24680-1
• Support Opportunities: Scholarships in Brazil - Doctorate
• Effective date (Start): April 01, 2018
• Effective date (End): December 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Llohann Dallagnol Sperança
• Grantee: Leonardo Francisco Cavenaghi
• 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

Abstract

A procedure commonly used to construct metrics of positive or non-negative sectional curvature is the Cheeger deformation. The aim of this project is to base a generalization of this deformation, tracing its parallel with geometric analysis, in order to obtain obstruction or/and sufficient conditions for positive/nonnegative sectional curvature on principal bundles and other families of manifolds. It is also intended to study the existence of metrics with prescribed scalar curvature and Einstein metrics. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CAVENAGHI, Leonardo Francisco. On metric deformations and applications. 2020. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.