New aspects on CR-structures of codimension 2 on hypersurfaces of Sasakian manifolds

Marian-Ioan Munteanu

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 1, page 69-84
  • ISSN: 0044-8753

Abstract

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We introduce a torsion free linear connection on a hypersurface in a Sasakian manifold on which we have defined in natural way a C R -structure of C R -codimension 2. We study the curvature properties of this connection and we give some interesting examples.

How to cite

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Munteanu, Marian-Ioan. "New aspects on CR-structures of codimension 2 on hypersurfaces of Sasakian manifolds." Archivum Mathematicum 042.1 (2006): 69-84. <http://eudml.org/doc/249777>.

@article{Munteanu2006,
abstract = {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.},
author = {Munteanu, Marian-Ioan},
journal = {Archivum Mathematicum},
keywords = {$CR-$structures; almost contact structures; $f$-structure with complemented frames; -structures; almost contact structures},
language = {eng},
number = {1},
pages = {69-84},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {New aspects on CR-structures of codimension 2 on hypersurfaces of Sasakian manifolds},
url = {http://eudml.org/doc/249777},
volume = {042},
year = {2006},
}

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
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 1
SP - 69
EP - 84
AB - 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.
LA - eng
KW - $CR-$structures; almost contact structures; $f$-structure with complemented frames; -structures; almost contact structures
UR - http://eudml.org/doc/249777
ER -

References

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  1. Blair D. E., Contact manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer-Verlag, 1976. (1976) Zbl0319.53026MR0467588
  2. Blair D. E., Riemannian geometry of contact and symplectic manifolds, Progr. Math. 203, Birkhäuser, 2001. Zbl1011.53001MR1874240
  3. Goldberg S. I., Yano K., On normal globally f -manifold, Tôhoku Math. J. 22 (1970), 362–370. (1970) MR0305295
  4. Lotta A., Pastore A. M., The Tanaka-Webster connection for almost S -manifolds and Cartan geometry, Arch. Math. (Brno) 40 (2004), 47–61. MR2054872
  5. Matzeu P., Oproiu V., The Bochner type curvature tensor of pseudoconvex C R structures, SUT J. Math. 31, 1 (1995), 1–16. (1995) MR1342761
  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. (1998) Zbl0916.53013MR1651570
  7. Yano K., Kon M., CR-submanifolds of Kählerian and Sasakian manifolds, Progr. Math. 30 (1983) Birkhäuser, Boston, Basel, Stuttgart. (1983) Zbl0496.53037MR0688816

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