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Publications [#243384] of Robert Bryant


Papers Published

  1. Bryant, RL, Harmonic morphisms with fibers of dimension one, Communications in Analysis and Geometry, vol. 8 no. 2 (January, 2000), pp. 219-265, International Press of Boston [MR2001i:53101], [dg-ga/9701002], [doi]
    (last updated on 2019/05/23)

    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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