Harmonic morphisms with fibers of dimension one
Repository Usage Stats
The harmonic morphisms φ : Mn+1 → Nn are studied using the methods of the moving frame and exterior differential systems and three main results are achieved. The first result is a local structure theorem for such maps in the case that φ is a submersion, in particular, a normal form is found for all such φ once the metric on the target manifold N is specified. The second result is a finiteness theorem, which says, in a certain sense, that, when n ≥ 3, the set of harmonic morphisms with a given Riemannian domain (Mn+1,g) is a finite dimensional space. The third result is the explicit classification when n ≥ 3 of all local and global harmonic morphisms with domain (Mn+1,g), a space of constant curvature.
More InfoShow full item record
Phillip Griffiths Professor of Mathematics
My research concerns problems in the geometric theory of partial differential equations. More specifically, I work on conservation laws for PDE, Finsler geometry, projective geometry, and Riemannian geometry, including calibrations and the theory of holonomy. Much of my work involves or develops techniques for studying systems of partial differential equations that arise in geometric problems. Because of their built-in invariance properties, these systems often have specia