https://doi.org/10.1140/epjb/e2002-00289-3
Some geometric aspects of CPN-1 maps
Department of Mathematical Sciences, University of Durham,
Durham DH1 3LE, UK
Corresponding author: a w.j.zakrzewski@durham.ac.uk
Received:
1
August
2001
Revised:
18
October
2001
Published online:
2
October
2002
In this talk we introduce a Weierstrass-like system of equations corresponding
to 
fields in two dimensions. Then using this representation
we introduce a vector 
in 
and treating this vector
as the radius vector of a surface immersed in we discuss to what extent the associated metric describes the geometry of the maps.
We show that for the holomorphic maps – the correspondence is exact;
while for the more general fields we have to go beyond the Weierstrass system and add extra terms.
PACS: 02.40.-K – Geometry, differential geometry, and topology / 02.30.Jr – Partial differential equations / 11.10.Lm – Nonlinear or nonlocal theories and models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
