Complex-valued differential forms on normal contact Riemannian manifolds

Fujitani, Tamehiro

doi:10.2748/tmj/1178243376

Cited by 28 publications

(19 citation statements)

References 4 publications

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“…There are some well-known topological obstructions to the existence of a Sasakian structure on a compact K-contact manifold (refer to, e.g. [6,2,4,9,1]). …”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Examples of simply-connected K-contact non-Sasakian manifolds of dimension 5

Kim

2015

Int. J. Geom. Methods Mod. Phys.

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The existence of compact simply-connected K-contact, but not Sasakian, manifolds has been unknown only for dimension 5. The aim of this paper is to show that the Kollár's simply-connected example which is a Seifert bundle over the complex projective space CP 2 and does not carry any Sasakian structure is actually a K-contact manifold. As a consequence, we affirmatively answer the above existence problem in dimension 5, establishing that there are infinitely many compact simply-connected K-contact manifolds of dimension 5 which do not carry a Sasakian structure.

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“…There are some well-known topological obstructions to the existence of a Sasakian structure on a compact K-contact manifold (refer to, e.g. [6,2,4,9,1]). …”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Examples of simply-connected K-contact non-Sasakian manifolds of dimension 5

Kim

2015

Int. J. Geom. Methods Mod. Phys.

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“…When ψ is the identity operator I : T M → T M , the operator i ψ will be denoted by deg, motivated by the fact that for any p-form ω we have deg ω = i I ω = pω. Now we summarize several results from [9] on commutators between operators on Ω * (M ), where M is a Sasakian manifold (N.B. : Fujitani uses Φ for i φ , ϕ for Φ, λ for i ξ , and l for ǫ η ).…”

Section: Preliminariesmentioning

confidence: 98%

“…There is a simple extension to Lefschetz contact manifolds of the wellknown property that the odd Betti numbers b 2k+1 (0 ≤ 2k + 1 ≤ n) of compact Sasakian manifolds are even ( [9]). Note that…”

Section: Lefschetz Contact Manifoldsmentioning

confidence: 99%

Hard Lefschetz theorem for Sasakian manifolds

Cappelletti–Montano¹,

Nicola²,

Yudin³

2015

J. Differential Geom.

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We prove that on a compact Sasakian manifold (M, η, g) of dimension 2n+1, for any 0 ≤ p ≤ n the wedge product with η ∧(dη) p defines an isomorphism between the spaces of harmonic forms Ω n−p ∆ (M ) and Ω n+p+1 ∆ (M ). Therefore it induces an isomorphism between the de Rham cohomology spaces H n−p (M ) and H n+p+1 (M ). Such isomorphism is proven to be independent of the choice of a compatible Sasakian metric on a given contact manifold. As a consequence, an obstruction for a contact manifold to admit Sasakian structures is found.

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“…It is known that any compact Sasakian manifold has even first Betti number; see [4,19,39]. Since one can lift a Sasakian structure to the covering space of a Sasakian manifold, the following proposition is immediate.…”

Section: R(x ξ)Y = G ξ Y X − G X Y ξmentioning

confidence: 89%

On the fundamental groups of compact Sasakian manifolds

Chen

2013

Mathematical Research Letters

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Abstract. We study the fundamental groups of compact Sasakian manifolds, which we call Sasaki groups. It is shown that the fundamental group of any compact Hodge manifold is Sasaki. In particular, all finite groups are Sasaki. On the other hand, we show that there exist many restrictions on Sasaki groups. We also study the Abel-Jacobi map of a compact Sasakian manifold and its applications to Sasaki groups.

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Complex-valued differential forms on normal contact Riemannian manifolds

Cited by 28 publications

References 4 publications

Examples of simply-connected K-contact non-Sasakian manifolds of dimension 5

Examples of simply-connected K-contact non-Sasakian manifolds of dimension 5

Hard Lefschetz theorem for Sasakian manifolds

On the fundamental groups of compact Sasakian manifolds

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