On CP 1 and CP 2 Maps and Weierstrass Representations for Surfaces Immersed into Multi-Dimensional Euclidean Spaces

DOI

10.2991/jnmp.2003.10.1.9How to use a DOI?

Abstract

An extension of the classic Enneper­Weierstrass representation for conformally prametrised surfaces in multi-dimensional spaces is presented. This is based on low dimensional CP1 and CP2 sigma models which allow the study of the constant mean curvature (CMC) surfaces immersed into Euclidean 3- and 8-dimensional spaces, rspectively. Relations of Weierstrass type systems to the equations of these sigma models are established. In particular, it is demonstrated that the generalised Weiestrass representation can admit different CMC-surfaces in R3 which have globally the same Gauss map. A new procedure for constructing CMC-surfaces in Rn is presented and illustrated in some explicit examples.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - A.M. Grundland
AU  - W.J. Zakrzewski
PY  - 2003
DA  - 2003/02/01
TI  - On CP 1 and CP 2 Maps and Weierstrass Representations for Surfaces Immersed into Multi-Dimensional Euclidean Spaces
JO  - Journal of Nonlinear Mathematical Physics
SP  - 110
EP  - 135
VL  - 10
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2003.10.1.9
DO  - 10.2991/jnmp.2003.10.1.9
ID  - Grundland2003
ER  -