Geodesic
New aspects on CR-structures of codimension 2 on hypersurfaces of Sasakian manifolds
Archivum mathematicum, Tome 42 (2006) no. 1, pp. 69-84 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 53C25, 53C40
Keywords: $CR-$structures; almost contact structures; $f$-structure with complemented frames 
@article{ARM_2006_42_1_a7,
     author = {Munteanu, Marian-Ioan},
     title = {New aspects on {CR-structures} of codimension 2 on hypersurfaces of {Sasakian} manifolds},
     journal = {Archivum mathematicum},
     pages = {69--84},
     year = {2006},
     volume = {42},
     number = {1},
     mrnumber = {2227114},
     zbl = {1164.53355},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a7/}
}
TY  - JOUR
AU  - Munteanu, Marian-Ioan
TI  - New aspects on CR-structures of codimension 2 on hypersurfaces of Sasakian manifolds
JO  - Archivum mathematicum
PY  - 2006
SP  - 69
EP  - 84
VL  - 42
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a7/
LA  - en
ID  - ARM_2006_42_1_a7
ER  - 
%0 Journal Article
%A Munteanu, Marian-Ioan
%T New aspects on CR-structures of codimension 2 on hypersurfaces of Sasakian manifolds
%J Archivum mathematicum
%D 2006
%P 69-84
%V 42
%N 1
%U http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a7/
%G en
%F ARM_2006_42_1_a7
Munteanu, Marian-Ioan. New aspects on CR-structures of codimension 2 on hypersurfaces of Sasakian manifolds. Archivum mathematicum, Tome 42 (2006) no. 1, pp. 69-84. http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a7/

[1] Blair D. E.: Contact manifolds in Riemannian Geometry. Lecture Notes in Math. 509, Springer-Verlag, 1976. | MR | Zbl

[2] Blair D. E.: Riemannian geometry of contact and symplectic manifolds. Progr. Math. 203, Birkhäuser, 2001. | MR | Zbl

[3] Goldberg S. I., Yano K.: On normal globally $f$-manifold. Tôhoku Math. J. 22 (1970), 362–370. | MR

[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

[5] Matzeu P., Oproiu V.: The Bochner type curvature tensor of pseudoconvex $CR$ structures. SUT J. Math. 31, 1 (1995), 1–16. | MR

[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. | MR | Zbl

[7] Yano K., Kon M.: CR-submanifolds of Kählerian and Sasakian manifolds. Progr. Math. 30 (1983) Birkhäuser, Boston, Basel, Stuttgart. | MR | Zbl