| Title:
|
Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II (English) |
| Author:
|
Lee, Hyunjin |
| Author:
|
Kim, Seonhui |
| Author:
|
Suh, Young Jin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
133-148 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces $M$ of Type ${\rm (A)}$ in complex two plane Grassmannians $G_2({\mathbb C}^{m+2})$ with a commuting condition between the shape operator $A$ and the structure tensors $\phi $ and $\phi _{1}$ for $M$ in $G_2({\mathbb C}^{m+2})$. Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator $A$ and a new operator $\phi \phi _{1}$ induced by two structure tensors $\phi $ and $\phi _{1}$. That is, this commuting shape operator is given by $\phi \phi _{1} A = A \phi \phi _{1}$. Using this condition, we prove that $M$ is locally congruent to a tube of radius $r$ over a totally geodesic $G_2({\mathbb C}^{m+1})$ in $G_2({\mathbb C}^{m+2})$. (English) |
| Keyword:
|
complex two-plane Grassmannians |
| Keyword:
|
Hopf hypersurface |
| Keyword:
|
$\mathfrak D^{\bot }$-invariant hypersurface |
| Keyword:
|
commuting shape operator |
| Keyword:
|
Reeb vector field |
| MSC:
|
32V40 |
| MSC:
|
53C15 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 06391482 |
| idMR:
|
MR3247450 |
| DOI:
|
10.1007/s10587-014-0089-6 |
| . |
| Date available:
|
2014-09-29T09:43:52Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143955 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/143029 |
| . |
| Reference:
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