Geometry and topology of Riemannian varieties

• Grant number: 93/00557-0
• Support Opportunities: Research Projects - Thematic Grants
• Start date: May 01, 1994
• End date: April 30, 1996
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Francesco Mercuri
• Grantee: Francesco Mercuri
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant(s): 96/01644-1 - Juno Mukai | Shinshu University - Japão, AV.EXT; 95/02527-6 - Maria Helena Noronha | California State University Northridge - Estados Unidos, AV.EXT

Abstract

The general objective of this project is the study of the topology of the Riemannian varieties with extrinsic and intrinsic metric restrictions. The principal topics are: a) sub-varieties of the IRn with non-negative curvature operator or with second fundamental form parallel; b) construction of metrics with non-negative curvature in fibered varieties; c) relationship of the items above with variational methods, including the energy functions, of Yang-Mills, of area and volume, with or without link, which includes harmonic applications; d) generalized theory of Morse and the study of orbits of Lie groups in the context above. (AU)