A note on the generalized Weierstrass representation

2002/07/27 by L. Martina, Martina, L., Kur. Myrzakul +3
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.math/0207261

8 pages, LateX

arxiv created 2002/07/27 · arxiv updated 2009/11/30

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 R⁸ with Euclidean metric.

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