Rigidity, characterization and construction of metrics on smooth manifolds

• Grant number: 23/11126-7
• Support Opportunities: Regular Research Grants
• Duration: December 01, 2023 - November 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: José Nazareno Vieira Gomes
• Grantee: José Nazareno Vieira Gomes
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The project is divided into four parts. In the first one, we will work on geometric identities and their applications to problems of rigidity in smooth manifolds with boundary. In the second one, we will deal with a possible way for constructing gradient Ricci solitons that are realized as warped metric on bundles. In the third one, we will address the rigidity problem of gradient shrinking Ricci solitons. The fourth one is a study of geometric and analytical aspects of the Ricci-Bourguignon flow, which includes a possible classification of particular classes of self-similar solutions of this flow. (AU)