| Title:
|
The dimension function of holomorphic spaces of a real submanifold of an almost complex manifold (English) |
| Author:
|
Etayo, Fernando |
| Author:
|
Fioravanti, Mario |
| Author:
|
Trías, Ujué R. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
139-141 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $ M $ be a real submanifold of an almost complex manifold $ (\overline{M},\overline{J}) $ and let $ H_{x}=T_{x}M\cap \overline{J}(T_{x}M) $ be the maximal holomorphic subspace, for each $ x\in M $. We prove that $ c\:M\rightarrow \mathbb{N} $, $ c(x)=\dim _{\mathbb{R}} H_{x} $ is upper-semicontinuous. (English) |
| Keyword:
|
holomorphic space |
| Keyword:
|
submanifold |
| Keyword:
|
almost complex |
| MSC:
|
53C15 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 1079.53504 |
| idMR:
|
MR1814639 |
| . |
| Date available:
|
2009-09-24T10:40:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127633 |
| . |
| Reference:
|
[C] B. Y. Chen: Geometry of Submanifolds and its Applications.Sci. Univ. Tokyo, 1981. Zbl 0474.53050, MR 0627323 |
| Reference:
|
[K-N] S. Kobayashi and K. Nomizu: Foundations of Differential Geometry, II.Interscience, New York, 1969. |
| Reference:
|
[W] R. O. Wells, Jr.: Differential Analysis on Complex Manifolds.Springer, New York, 1980. Zbl 0435.32004, MR 0608414 |
| . |
