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A simple way for determining the normalized potentials for harmonic maps. (English) Zbl 0954.58017

A surface in \(R^3\) is called CMC-surface if it is an immersed constant mean curvature \(H={1\over 2}\) surface in \(R^3\).
The main result of this paper is to give a simple way for determining the normalized potentials, in the Weierstrass type representation of the harmonic maps from a Riemann surface to a compact symmetric space. As a direct application, the author obtains the normalized potential for an arbitrary CMC-surface in terms of its Hopf differential and the holomorphic part of its induced metric. Moreover, the author mentions some results related to the normalized potential which can be used to study invariants of the dressing action of loop groups on harmonic maps. For related results see J. Dorfmeister and G. Haak [Math. Z., to appear], J. Dorfmeister, I. McIntosh, F. Pedit and H. Wu [Manuscr. Math. 92, No. 2, 143-152 (1997; Zbl 0903.58005)] and H. Wu [Tôhoku Math. J., II. Ser. 49, No. 4, 599-621 (1997; Zbl 0912.53010)].
Reviewer: C.-J.Sung

MSC:

58E20 Harmonic maps, etc.
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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