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Geometrical aspects of the complex eikonal equations associated to the generalized Weierstrass representation

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Czechoslovak Journal of Physics Aims and scope

Abstract

Certain geometrical aspects of a Laplace-Beltrami equation subjected to a complex eikonal equation are studied. It is shown that all principal curvatures of a solution surface are constant for this system. To illustrate the theoretical considerations, we look for a class of solutions of an overdetermined system composed of the sigma model and a system of complex eikonal equations. The connection between the sigma model and the generalized Weierstrass system for inducing constant mean curvature surfaces allows us to construct special classes of solutions for classical configurations of strings.

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Authors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, C. P. 6128 Succ. Centre Ville, H3C 3J7, Montréal, QC, Canada

    P. Bracken & A. M. Grundland

Authors
  1. P. Bracken
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  2. A. M. Grundland
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Additional information

This work was supported by a research grant from NSERC of Canada and the hospitality of the Doppler Institute of the Czech Republic.

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Bracken, P., Grundland, A.M. Geometrical aspects of the complex eikonal equations associated to the generalized Weierstrass representation. Czech J Phys 51, 293–300 (2001). https://doi.org/10.1023/A:1017529203946

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  • DOI: https://doi.org/10.1023/A:1017529203946

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