The Tanaka-Webster connection for almost 𝒮 -manifolds and Cartan geometry

Antonio Lotta; Anna Maria Pastore

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 1, page 47-61
  • ISSN: 0044-8753

Abstract

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We prove that a CR-integrable almost 𝒮 -manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost 𝒮 -structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost 𝒮 -structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal almost 𝒮 -manifolds with higher CR-codimension, whose Tanaka–Webster curvature vanishes.

How to cite

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Lotta, Antonio, and Pastore, Anna Maria. "The Tanaka-Webster connection for almost $\mathcal {S}$-manifolds and Cartan geometry." Archivum Mathematicum 040.1 (2004): 47-61. <http://eudml.org/doc/249303>.

@article{Lotta2004,
abstract = {We prove that a CR-integrable almost $\mathcal \{S\}$-manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost $\mathcal \{S\}$-structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost $\mathcal \{S\}$-structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal almost $\mathcal \{S\}$-manifolds with higher CR-codimension, whose Tanaka–Webster curvature vanishes.},
author = {Lotta, Antonio, Pastore, Anna Maria},
journal = {Archivum Mathematicum},
keywords = {almost $\mathcal \{S\}$-structure; Tanaka–Webster connection; Cartan connection; CR manifold; almost -structure; Cartan connection},
language = {eng},
number = {1},
pages = {47-61},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The Tanaka-Webster connection for almost $\mathcal \{S\}$-manifolds and Cartan geometry},
url = {http://eudml.org/doc/249303},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Lotta, Antonio
AU - Pastore, Anna Maria
TI - The Tanaka-Webster connection for almost $\mathcal {S}$-manifolds and Cartan geometry
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 1
SP - 47
EP - 61
AB - We prove that a CR-integrable almost $\mathcal {S}$-manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost $\mathcal {S}$-structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost $\mathcal {S}$-structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal almost $\mathcal {S}$-manifolds with higher CR-codimension, whose Tanaka–Webster curvature vanishes.
LA - eng
KW - almost $\mathcal {S}$-structure; Tanaka–Webster connection; Cartan connection; CR manifold; almost -structure; Cartan connection
UR - http://eudml.org/doc/249303
ER -

References

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