## The local structure of trans-Sasakian manifolds.(English)Zbl 0772.53036

A trans-Sasakian structure is, in some sense, an analogue of a locally conformal Kähler structure on an almost Hermitian manifold. Two remarkable subclasses of trans-Sasakian structures are those called $${\mathcal C}_ 5$$- and $${\mathcal C}_ 6$$-structures, which contain the Kenmotsu and Sasakian structures respectively. In this paper the author has completely characterized the local nature of trans-Sasakian structures on differentiable manifolds of dimension $$\geq 5$$. This has been done through two stages: 1) characterizing the local nature of $${\mathcal C}_ 5$$- and $${\mathcal C}_ 6$$-structures; 2) showing that a trans- Sasakian structure is either of class $${\mathcal C}_ 5$$ or of class $${\mathcal C}_ 6$$. The author has finally obtained some examples of 3-dimensional trans-Sasakian manifolds which are neither of class $${\mathcal C}_ 5$$ nor of class $${\mathcal C}_ 6$$.
Reviewer: N.L.Youssef (Giza)

### MSC:

 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)

### Keywords:

Kenmotsu structure; conformal Kähler structure
Full Text:

### References:

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