Minimal submanifolds in 4 with a g.c.K. structure

Marian-Ioan Munteanu

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 1, page 61-78
  • ISSN: 0011-4642

Abstract

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In this paper we obtain all invariant, anti-invariant and C R submanifolds in ( 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.

How to cite

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Munteanu, Marian-Ioan. "Minimal submanifolds in $\mathbb {R}^4$ with a g.c.K. structure." Czechoslovak Mathematical Journal 58.1 (2008): 61-78. <http://eudml.org/doc/31199>.

@article{Munteanu2008,
abstract = {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.},
author = {Munteanu, Marian-Ioan},
journal = {Czechoslovak Mathematical Journal},
keywords = {locally conformal Kähler structure; minimal submanifolds; invariant submanifolds; totally real submanifolds; $CR$-submanifolds; locally conformal Kähler structure; invariant submanifolds; totally real submanifolds; -submanifolds},
language = {eng},
number = {1},
pages = {61-78},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Minimal submanifolds in $\mathbb \{R\}^4$ with a g.c.K. structure},
url = {http://eudml.org/doc/31199},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Munteanu, Marian-Ioan
TI - Minimal submanifolds in $\mathbb {R}^4$ with a g.c.K. structure
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 1
SP - 61
EP - 78
AB - 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.
LA - eng
KW - locally conformal Kähler structure; minimal submanifolds; invariant submanifolds; totally real submanifolds; $CR$-submanifolds; locally conformal Kähler structure; invariant submanifolds; totally real submanifolds; -submanifolds
UR - http://eudml.org/doc/31199
ER -

References

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  1. 10.2206/kyushujm.56.337, Kyushu J.  Math. 56 (2002), 337–362. (2002) MR1934130DOI10.2206/kyushujm.56.337
  2. Locally Conformal Kähler Geometry, Birkhäuser-Verlag, Boston-Basel-Berlin, 1998. (1998) MR1481969
  3. 10.1007/BF00147450, Geom. Dedicata 28 (1988), 181–197. (1988) Zbl0659.53041MR0971624DOI10.1007/BF00147450
  4. 4 -dimensional Kählerian manifolds, Preprint  2004. 
  5. 10.1007/BF02412833, Ann. Mat. Pura Appl. 36 (1954), 27–120. (French) (1954) MR0066020DOI10.1007/BF02412833
  6. 10.1007/BF02834764, Isr. J.  Math. 24 (1976), 338–351. (1976) Zbl0335.53055MR0418003DOI10.1007/BF02834764
  7. C R   Submanifolds of Kaehlerian and Sasakian Manifolds, Birkhäuser-Verlag, Boston-Basel-Stuttgart, 1983. (1983) MR0688816

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