Harmonic morphisms with fibers of dimension one
Abstract
Description
I prove three classification results about harmonic morphisms whose fibers have dimension one. All are valid when the domain is at least of dimension 4. (The character of this overdetermined problem is very different when the dimension of the domain is 3 or less.) The first result is a local classification for such harmonic morphisms with specified target metric, the second is a finiteness theorem for such harmonic morphisms with specified domain metric, and the third is a complete classification of such harmonic morphisms when the domain is a space form of constant sectional curvature
The methods used are exterior differential systems and the moving frame. The fundamental results are local, but, because of the rigidity of the solutions, they allow a complete global classification.
AMS-TeX v2.1, amsppt.sty (v. 2.1d), 36 pages. This is a slight revision of the original (2 January 97), containing some more references to the literature and incorporating a few minor typographical and grammatical corrections. (Thanks to J. Wood and S. Gudmundsson for their suggestions.)
AMS-TeX v2.1, amsppt.sty (v. 2.1d), 36 pages. This is a slight revision of the original (2 January 97), containing some more references to the literature and incorporating a few minor typographical and grammatical corrections. (Thanks to J. Wood and S. Gudmundsson for their suggestions.)