Notes on some classes of 3-dimensional contact metric manifolds

A review of the geometry of 3-dimensional contact metric manifolds shows that generalized Sasakian manifolds and [eta]-Einstein manifolds are deeply interrelated. For example, it is known that a 3-dimensional Sasakian manifold is [eta]-Einstein. In this paper, we discuss the relationships between se...

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Bibliographic Details
Published in:Balkan journal of geometry and its applications 2012-01, Vol.17 (2), p.54
Main Authors: Jin, J.E, Park, J.H, Sekigawa, K
Format: Article
Language:English
Subjects:
Manifolds (Mathematics)
Metric spaces
Online Access:Get full text
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Summary:A review of the geometry of 3-dimensional contact metric manifolds shows that generalized Sasakian manifolds and [eta]-Einstein manifolds are deeply interrelated. For example, it is known that a 3-dimensional Sasakian manifold is [eta]-Einstein. In this paper, we discuss the relationships between several special classes of 3-dimensional contact metric manifolds which are generalizations of 3-dimensional Sasakian manifolds. We also provide examples illustrating our result in this paper. M.S.C. 2010: 53D10, 53C25. Key words: Sasakian manifolds; contact metric manifolds.
ISSN:1224-2780