Minimal submanifolds in \(\mathbb R^4\) with a g.c. K. structure. (English) Zbl 1174.53011

Summary: In this paper we obtain all invariant, anti-invariant and \(CR\) submanifolds in  \((\mathbb R^4,g,J)\) endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c. K. structure.


53B25 Local submanifolds
53B35 Local differential geometry of Hermitian and Kählerian structures
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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