Harmonic morphisms with fibers of dimension one

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Bryant, RL

Published Date

  • January 1, 2000

Published In

Volume / Issue

  • 8 / 2

Start / End Page

  • 219 - 265

International Standard Serial Number (ISSN)

  • 1019-8385

Digital Object Identifier (DOI)

  • 10.4310/CAG.2000.v8.n2.a1

Citation Source

  • Scopus