Math @ Duke

Publications [#243384] of Robert Bryant
search www.ams.org.Papers Published
 Bryant, RL, Harmonic morphisms with fibers of dimension one,
Communications in Analysis and Geometry, vol. 8 no. 2
(January, 2000),
pp. 219265, International Press of Boston [MR2001i:53101], [dgga/9701002], [doi]
(last updated on 2019/08/19)
Abstract: 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.


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