Communications in Analysis and Geometry

Volume 15 (2007)

Number 2

Minimal Lagrangian surfaces in $\Bbb S\sp 2 x $\Bbb S\sp 2$

Pages: 217 – 248

DOI: http://dx.doi.org/10.4310/CAG.2007.v15.n2.a1

Authors

Ildefonso Castro

Francisco Urbano

Abstract

We deal with the minimal Lagrangian surfaces of the Einstein-Kähler $\Bbb S\sp 2 x \Bbb S\sp 2$ surface, studying local geometric properties and showing that they can be locally described as Gauss maps of minimal surfaces in $\Bbb S\sp 2 \subset \Bbb R\sp 4$ . We also discuss the second variation of the area and characterize the most relevant examples by their stability behaviour.

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