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A CLASSIFICATION OF SPHERICAL SYMMETRIC CR MANIFOLDS

Part of: Global differential geometry

Published online by Cambridge University Press:  08 June 2009

G. DILEO  and
A. LOTTA
G. DILEO
Affiliation:
Dipartimento di Matematica, Università di Bari, Via E. Orabona 4, 70125 Bari, Italy (email: dileo@dm.uniba.it)
A. LOTTA*
Affiliation:
Dipartimento di Matematica, Università di Bari, Via E. Orabona 4, 70125 Bari, Italy (email: lotta@dm.uniba.it)
*
✉For correspondence; e-mail: lotta@dm.uniba.it
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Abstract

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In this paper we get different characterizations of the spherical strictly pseudoconvex CR manifolds admitting a CR-symmetric Webster metric by means of the Tanaka–Webster connection and of the Riemannian curvature tensor. As a consequence we obtain the classification of the simply connected, spherical symmetric pseudo-Hermitian manifolds.

Keywords

CR-symmetric spacespherical CR manifoldcontact Riemannian (k,μ)-spaceBochner curvature tensor

MSC classification

Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C35: Symmetric spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 2 , October 2009 , pp. 251 - 274
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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