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The Structure of Some Classes of Contact Metric Manifolds

The Structure of Some Classes of Contact Metric Manifolds We study the conformal curvature tensor and the contact conformal curvature tensor in Sasakian and/or K -contact manifolds. We find a necessary and sufficient condition for a Sasakian manifold to be φ -conformally flat. We also find some necessary conditions for a K -contact manifold to be φ -contact conformally flat. Then we give a structure theorem for φ -contact conformally flat Sasakian manifolds. It is also proved that a Sasakian manifold cannot be ξ -contact conformally flat. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

The Structure of Some Classes of Contact Metric Manifolds

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References (11)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2009.295
Publisher site
See Article on Publisher Site

Abstract

We study the conformal curvature tensor and the contact conformal curvature tensor in Sasakian and/or K -contact manifolds. We find a necessary and sufficient condition for a Sasakian manifold to be φ -conformally flat. We also find some necessary conditions for a K -contact manifold to be φ -contact conformally flat. Then we give a structure theorem for φ -contact conformally flat Sasakian manifolds. It is also proved that a Sasakian manifold cannot be ξ -contact conformally flat.

Journal

Georgian Mathematical Journalde Gruyter

Published: Jun 1, 2009

Keywords: K -contact manifold; Sasakian manifold; conformal curvature tensor; contact conformal curvature tensor

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