Rigidity, characterization and construction of metrics on smooth manifolds

• Grant number: 23/11126-7
• Support Opportunities: Regular Research Grants
• Start date: December 01, 2023
• End date: 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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

AGILA, ENRIQUE F. L.; GOMES, JOSE N. V.. Geometric and analytic results for Einstein solitons. Mathematische Nachrichten, v. 297, n. 8, p. 18-pg., 2024-04-10. (23/11126-7)

GOMES, JOSE NAZARENO VIEIRA; TOKURA, WILLIAN ISAO. Gradient Einstein-type warped products: Rigidity, existence and nonexistence results via a nonlinear PDE. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 255, p. 20-pg., 2025-06-01. (23/11126-7)