| 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:
|
http://hdl.handle.net/10338.dmlcz/128246 |
| . |
| Reference:
|
[1] D. E. Blair, S. Dragomir: $CR$-products in Locally Conformal Kähler Manifolds.Kyushu J. Math. 56 (2002), 337–362. MR 1934130, 10.2206/kyushujm.56.337 |
| 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 |
| . |
