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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.

MSC:

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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References:

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