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Title: Minimal submanifolds in $\mathbb{R}^4$ with a g.c.K. structure (English)
Author: Munteanu, Marian-Ioan
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 1
Year: 2008
Pages: 61-78
Summary lang: English
Category: math
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. (English)
Keyword: locally conformal Kähler structure
Keyword: minimal submanifolds
Keyword: invariant submanifolds
Keyword: totally real submanifolds
Keyword: $CR$-submanifolds
MSC: 53B25
MSC: 53B35
MSC: 53C21
MSC: 53C42
MSC: 53C55
idZBL: Zbl 1174.53011
idMR: MR2402526
Date available: 2009-09-24T11:53:36Z
Last updated: 2020-07-03
Stable URL:
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Reference: [2] S.  Dragomir, L.  Ornea: Locally Conformal Kähler Geometry.Birkhäuser-Verlag, Boston-Basel-Berlin, 1998. MR 1481969
Reference: [3] S.  Dragomir: Cauchy-Riemann submanifolds of locally conformal Kaehler manifolds.Geom. Dedicata 28 (1988), 181–197. Zbl 0659.53041, MR 0971624, 10.1007/BF00147450
Reference: [4] H.  Inage, K.  Matsumoto: $4$-dimensional Kählerian manifolds.Preprint  2004.
Reference: [5] P.  Libermann: Sur le problème d’équivalence de certaines structures infinitésimales régulières.Ann. Mat. Pura Appl. 36 (1954), 27–120. (French) MR 0066020, 10.1007/BF02412833
Reference: [6] I.  Vaisman: On locally conformal almost Kähler manifolds.Isr. J.  Math. 24 (1976), 338–351. Zbl 0335.53055, MR 0418003, 10.1007/BF02834764
Reference: [7] K.  Yano, M.  Kon: $CR$  Submanifolds of Kaehlerian and Sasakian Manifolds.Birkhäuser-Verlag, Boston-Basel-Stuttgart, 1983. MR 0688816


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