Geodesic
Minimal submanifolds in $\mathbb{R}^4$ with a g.c.K. structure
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 61-78.

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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.
Classification : 53B25, 53B35, 53C21, 53C42, 53C55
Keywords: locally conformal Kähler structure; minimal submanifolds; invariant submanifolds; totally real submanifolds; $CR$-submanifolds 
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     author = {Munteanu, Marian-Ioan},
     title = {Minimal submanifolds in $\mathbb{R}^4$ with a {g.c.K.} structure},
     journal = {Czechoslovak Mathematical Journal},
     pages = {61--78},
     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {2008},
     mrnumber = {2402526},
     zbl = {1174.53011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008__58_1_a4/}
}
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Munteanu, Marian-Ioan. Minimal submanifolds in $\mathbb{R}^4$ with a g.c.K. structure. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 61-78. http://geodesic.mathdoc.fr/item/CMJ_2008__58_1_a4/