On simply connected \(K\)-contact non-Sasakian manifolds. (English) Zbl 1320.53097
The main result of this paper is to solve the following problem posed by C. P. Boyer and K. Galicki see, Open Problem 7.4 on page 235 in their book; [Sasakian geometry. Oxford: Oxford University Press (2008; Zbl 1155.53002)]: Do there exist simply connected closed \(K\)-contact manifolds with no Sasakian structure? The authors answer this question positively. They prove that such manifolds do exist using the method of fat bundles developed in the framework of symplectic and contact geometry by Sternberg, Weinstein and Lerman.
Reviewer: Ahmed Lesfari (El Jadida)
MSC:
| 53D05 | Symplectic manifolds (general theory) |
Keywords:
fat bundle; \(K\)-contact manifold; Sasakian manifold; symplectic manifold; contact manifoldCitations:
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