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Examples of unstable Hamiltonian-minimal Lagrangian tori in $C^2$

Published online by Cambridge University Press:  04 December 2007

ILDEFONSO CASTRO
Affiliation:
Departamento de Matemáticas, Escuela Politécnica Superior, Universidad de Jaén, 23071 Jén, Spain. e-mail: icastro@ujaen.es
FRANCISCO URBANO
Affiliation:
Departamento de Geometría y Topoligia, Universidad de Granada, 18071 Granada, Spain. e-mail: furbano@goliat.ugr.es
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Abstract

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A new family of Hamiltonian-minimal Lagrangian tori in the complex Euclidean plane is constructed. They are the first known unstable ones and are characterized in terms of being the only Hamiltonian-minimal Lagrangian tori (with non-parallel mean curvature vector) in $C^2$ admitting a one-parameter group of isometries.

Type
Research Article
Copyright
1998 Kluwer Academic Publishers