Research Profile: Differential Geometry, Riemannian geometry & Applications
My research deals with some aspects of the curvature of a Riemannian
manifold, in particular the way various curvature assumptions influence the
topological properties. There are several groups of theorems that address this
question, and my contribution belongs to Pinching Theorems. The method I used
consists of studying special flow of metrics whose property is that the reduced
curvature tensor changes according to the heat equation.
I have also employed the tools of Riemannian geometry (especially foliations
on Riemannian manifolds) in order to study the properties of orbits of vector
fields coming from various control theory problems.
In collaboration with Ernst Ruh and Maung Min-Oo, I have obtained new
parametrization of the space of multivariate normal distributions (and a new
distance formula) and am investigating futrher applications.