scholarly journals Examples of compact K-contact manifolds with no Sasakian metric

2014 ◽  
Vol 11 (09) ◽  
pp. 1460028 ◽  
Author(s):  
Beniamino Cappelletti-Montano ◽  
Antonio De Nicola ◽  
Juan Carlos Marrero ◽  
Ivan Yudin
Keyword(s):  
Sasakian Manifolds ◽  
Contact Manifolds ◽  
Lefschetz Theorem ◽  
Sasakian Metric ◽  
Hard Lefschetz Theorem

Using the hard Lefschetz theorem for Sasakian manifolds, we find two examples of compact K-contact nilmanifolds with no compatible Sasakian metric in dimensions 5 and 7, respectively.

scholarly journals Hard Lefschetz theorem for Sasakian manifolds

2015 ◽  
Vol 101 (1) ◽  
pp. 47-66 ◽  
Author(s):  
Beniamino Cappelletti-Montano ◽  
Antonio De Nicola ◽  
Ivan Yudin
Keyword(s):  
Sasakian Manifolds ◽  
Lefschetz Theorem ◽  
Hard Lefschetz Theorem

scholarly journals Invariance of basic Hodge numbers under deformations of Sasakian manifolds

2020 ◽  
Author(s):  
Paweł Raźny
Keyword(s):  
Elliptic Operators ◽  
Holomorphic Foliation ◽  
Sasakian Manifolds ◽  
Contact Manifolds ◽  
Continuity Theorem ◽  
Riemannian Foliations ◽  
Holomorphic Structure ◽  
Sasakian Structure ◽  
Hodge Numbers ◽  
Small Deformations

Abstract We show that the Hodge numbers of Sasakian manifolds are invariant under arbitrary deformations of the Sasakian structure. We also present an upper semi-continuity theorem for the dimensions of kernels of a smooth family of transversely elliptic operators on manifolds with homologically orientable transversely Riemannian foliations. We use this to prove that the $$\partial {\bar{\partial }}$$ ∂ ∂ ¯ -lemma and being transversely Kähler are rigid properties under small deformations of the transversely holomorphic structure which preserve the foliation. We study an example which shows that this is not the case for arbitrary deformations of the transversely holomorphic foliation. Finally we point out an application of the upper-semi continuity theorem to K-contact manifolds.

scholarly journals Hard Lefschetz theorem for Vaisman manifolds

2018 ◽  
Vol 371 (2) ◽  
pp. 755-776
Author(s):  
Beniamino Cappelletti-Montano ◽  
Antonio De Nicola ◽  
Juan Carlos Marrero ◽  
Ivan Yudin
Keyword(s):  
Lefschetz Theorem ◽  
Vaisman Manifolds ◽  
Hard Lefschetz Theorem
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