A simple way for determining the normalized potentials for harmonic maps (Q1284576)
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scientific article; zbMATH DE number 1278987
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple way for determining the normalized potentials for harmonic maps |
scientific article; zbMATH DE number 1278987 |
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A simple way for determining the normalized potentials for harmonic maps (English)
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13 June 1999
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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 \textit{J. Dorfmeister} and \textit{G. Haak} [Math. Z., to appear], \textit{J. Dorfmeister}, \textit{I. McIntosh}, \textit{F. Pedit} and \textit{H. Wu} [Manuscr. Math. 92, No. 2, 143-152 (1997; Zbl 0903.58005)] and \textit{H. Wu} [TĂ´hoku Math. J., II. Ser. 49, No. 4, 599-621 (1997; Zbl 0912.53010)].
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constant mean curvature
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normalized potentials
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Weierstrass type representation
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harmonic maps
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