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Article

Keywords:
$CR-$structures; almost contact structures; $f$-structure with complemented frames
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.
References:
[1] Blair D. E.: Contact manifolds in Riemannian Geometry. Lecture Notes in Math. 509, Springer-Verlag, 1976. MR 0467588 | Zbl 0319.53026
[2] Blair D. E.: Riemannian geometry of contact and symplectic manifolds. Progr. Math. 203, Birkhäuser, 2001. MR 1874240 | Zbl 1011.53001
[3] Goldberg S. I., Yano K.: On normal globally $f$-manifold. Tôhoku Math. J. 22 (1970), 362–370. MR 0305295
[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
[5] Matzeu P., Oproiu V.: The Bochner type curvature tensor of pseudoconvex $CR$ structures. SUT J. Math. 31, 1 (1995), 1–16. MR 1342761
[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 1651570 | Zbl 0916.53013
[7] Yano K., Kon M.: CR-submanifolds of Kählerian and Sasakian manifolds. Progr. Math. 30 (1983) Birkhäuser, Boston, Basel, Stuttgart. MR 0688816 | Zbl 0496.53037
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