Embeddability of some strongly pseudoconvex CR manifolds

Marinescu, George; Yeganefar, Nader

doi:10.1090/s0002-9947-07-04047-0

Cited by 20 publications

(19 citation statements)

References 30 publications

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“…If in addition the almost complex structure J is integrable, the 1-form is a Sasakian contact form, and the contact structure D is said to be of Sasaki type. We mention that contact structures of K-contact type are symplectically fillable [NP09], while those of Sasaki type are holomorphically fillable [MY07]. All contact structures discussed in this paper are of Sasaki type.…”

Section: Sasakian Structuresmentioning

confidence: 87%

On the equivalence problem for toric contact structures onS³-bundles overS²

Boyer

Pati

2014

Pacific J. Math.

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We study the contact equivalence problem for toric contact structures on S 3 -bundles over S 2 . That is, given two toric contact structures, one can ask the question: when are they equivalent as contact structures while inequivalent as toric contact structures? In general this appears to be a difficult problem. To find inequivalent toric contact structures that are contact equivalent, we show that the corresponding 3-tori belong to distinct conjugacy classes in the contactomorphism group. To show that two toric contact structures with the same first Chern class are contact inequivalent, we use Morse-Bott contact homology. We treat a subclass of contact structures which include the Sasaki-Einstein contact structures Y p,q studied by physicists in [GMSW04a, MS05, MS06]. In this subcase we give a complete solution to the contact equivalence problem by showing that Y p,q and Y p ′ q ′ are inequivalent as contact structures if and only if p = p ′ . for helpful discussions on toric geometry. The second author would like to thank Tobias Ekholm, Georgios Dimitroglou Rizell, and Clement Hyrvier for many useful discussions.

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Section: Sasakian Structuresmentioning

confidence: 87%

On the equivalence problem for toric contact structures onS³-bundles overS²

Boyer

Pati

2014

Pacific J. Math.

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“…Theorem 5.60 of [CE12], that a contact structure of Sasaki type is holomorphically fillable if the dimension of M is at least 5, and hence, Kähler fillable by Theorem 5.59 of [CE12]. The 3-dimensional case was later also shown to be holomorphically fillable by Marinescu and Yeganefar, [MY07]. Due to results of Bogomolov and de Oliveira, [BdO97], the 3-dimensional case then turns out to be Stein fillable.…”

Section: S 1 -Equivariant Symplectic Homology and Brieskorn Manifoldsmentioning

confidence: 99%

Brieskorn manifolds, positive Sasakian geometry, and contact topology

2015

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Abstract. Using S 1 -equivariant symplectic homology, in particular its mean Euler characteristic, of the natural filling of links of Brieskorn-Pham polynomials, we prove the existence of infinitely many inequivalent contact structures on various manifolds, including in dimension 5 the k-fold connected sums of S 2 × S 3 and certain rational homology spheres. We then apply our result to show that on these manifolds the moduli space of classes of positive Sasakian structures has infinitely many components. We also apply our results to give lower bounds on the number of components of the moduli space of Sasaki-Einstein metrics on certain homotopy spheres. Finally a new family of Sasaki-Einstein metrics of real dimension 20 on S 5 is exhibited.

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“…[MY,Consequence 3.2]). Let ∆ 1 be a unit disk in C. Averaging ψ with S 1 -action induced by ρ, we may assume that ψ is S 1 -invariant.…”

Section: Sasakian Manifolds In Algebraic Conesmentioning

confidence: 99%

Sasakian structures on CR-manifolds

Verbitsky

2007

Geom Dedicata

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A contact manifold M can be defined as a quotient of a symplectic manifold X by a proper, free action of R >0 , with the symplectic form homogeneous of degree 2. If X is, in addition, Kähler, and its metric is also homogeneous of degree 2, M is called Sasakian. A Sasakian manifold is realized naturally as a level set of a Kähler potential on a complex manifold, hence it is equipped with a pseudoconvex CR-structure. We show that any Sasakian manifold M is CR-diffeomorphic to an S 1 -bundle of unit vectors in a positive line bundle on a projective Kähler orbifold. This induces an embedding from M to an algebraic cone C. We show that this embedding is uniquely defined by the CRstructure. Additionally, we classify the Sasakian metrics on an odd-dimensional sphere equipped with a standard CR-structure.

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Embeddability of some strongly pseudoconvex CR manifolds

Cited by 20 publications

References 30 publications

On the equivalence problem for toric contact structures onS³-bundles overS²

On the equivalence problem for toric contact structures onS³-bundles overS²

Brieskorn manifolds, positive Sasakian geometry, and contact topology

Sasakian structures on CR-manifolds

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Embeddability of some strongly pseudoconvex CR manifolds

Cited by 20 publications

References 30 publications

On the equivalence problem for toric contact structures onS3-bundles overS2

On the equivalence problem for toric contact structures onS3-bundles overS2

Brieskorn manifolds, positive Sasakian geometry, and contact topology

Sasakian structures on CR-manifolds

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Resources

About

On the equivalence problem for toric contact structures onS³-bundles overS²

On the equivalence problem for toric contact structures onS³-bundles overS²