| Title:
|
New aspects on CR-structures of codimension 2 on hypersurfaces of Sasakian manifolds (English) |
| Author:
|
Munteanu, Marian-Ioan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
69-84 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce a torsion free linear connection on a hypersurface in a Sasakian manifold on which we have defined in natural way a $CR$-structure of $CR$-codimension 2. We study the curvature properties of this connection and we give some interesting examples. (English) |
| Keyword:
|
$CR-$structures |
| Keyword:
|
almost contact structures |
| Keyword:
|
$f$-structure with complemented frames |
| MSC:
|
53C25 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 1164.53355 |
| idMR:
|
MR2227114 |
| . |
| Date available:
|
2008-06-06T22:47:24Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107983 |
| . |
| Reference:
|
[1] Blair D. E.: Contact manifolds in Riemannian Geometry.Lecture Notes in Math. 509, Springer-Verlag, 1976. Zbl 0319.53026, MR 0467588 |
| Reference:
|
[2] Blair D. E.: Riemannian geometry of contact and symplectic manifolds.Progr. Math. 203, Birkhäuser, 2001. Zbl 1011.53001, MR 1874240 |
| Reference:
|
[3] Goldberg S. I., Yano K.: On normal globally $f$-manifold.Tôhoku Math. J. 22 (1970), 362–370. MR 0305295 |
| Reference:
|
[4] Lotta A., Pastore A. M.: The Tanaka-Webster connection for almost $S$-manifolds and Cartan geometry.Arch. Math. (Brno) 40 (2004), 47–61. MR 2054872 |
| Reference:
|
[5] Matzeu P., Oproiu V.: The Bochner type curvature tensor of pseudoconvex $CR$ structures.SUT J. Math. 31, 1 (1995), 1–16. MR 1342761 |
| Reference:
|
[6] Matzeu P., Oproiu V.: The Bochner type curvature tensor of pseudo-convex CR structures on real hypersurfaces in complex space forms.J. Geom. 63 (1998), 134–146. Zbl 0916.53013, MR 1651570 |
| Reference:
|
[7] Yano K., Kon M.: CR-submanifolds of Kählerian and Sasakian manifolds.Progr. Math. 30 (1983) Birkhäuser, Boston, Basel, Stuttgart. Zbl 0496.53037, MR 0688816 |
| . |
