The principal investigators will study several problems in global Riemannian geometry related to the existence, classification, and degeneration of compact Riemannian manifolds which are extremal for an integral norm of the curvature. They will also study applications of this theory to Kahler geometry, differential topology, and mathematical physics. One principal investigator will study the existence of degenerate solutions to the critical metric problem. The second principal investigator will study the holonomy of complete manifolds of positive scalar curvature. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9204093
Program Officer
James Glazebrook
Project Start
Project End
Budget Start
1992-06-01
Budget End
1996-05-31
Support Year
Fiscal Year
1992
Total Cost
$199,500
Indirect Cost
Name
State University New York Stony Brook
Department
Type
DUNS #
City
Stony Brook
State
NY
Country
United States
Zip Code
11794