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A note on the generalized Weierstrass representation

L. Martina·Kur. Myrzakul·R. Myrzakulov
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Abstract

The study of the relation between the Weierstrass inducing formulae for constant mean curvature surfaces and the completely integrable euclidean nonlinear sigma-model suggests a connection among integrable sigma -models in a background and other type of surfaces. We show how a generalization of the Weierstrass representation can be achieved and we establish a connection with the Weingarten surfaces. We suggest also a possible generalization for two-dimensional surfaces immersed in a flat space R^8 with Euclidean metric.

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L. Martina, Kur. Myrzakul, R. Myrzakulov. 2002-07-27. A note on the generalized Weierstrass representation. https://arxiv.org/abs/math/0207261

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