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Notes on some classes of 3-dimensional contact metric manifolds. (English) Zbl 1284.53075

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.

MSC:

53D10 Contact manifolds (general theory)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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