Construction and Classification of Isometric Minimal Immersions of Kähler Manifolds into Euclidean Spaces

Abstract

A classification of isometric minimal immersions of Kähler manifolds into Euclidean spaces is given, which is a generalization of the Calabi–Lawson theory concerning minimal surfaces. Moreover, we explicitly construct a nonholomorphic isometric minimal immersion of a complete Kähler manifold, biholomorphic to C2, into R6.