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Minimal submanifolds in $\mathbb{R}^4$ with a g.c.K. structure

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.