Results 11 to 20 of about 82 (82)

The range of the tangential Cauchy–Riemann system to a CR embedded manifold [PDF]

Inventiones mathematicae, 2012
We prove that every compact, pseudoconvex, orientable, CR manifold of $\C^n$, bounds a complex manifold in the $C^\infty$ sense. In particular, the tangential Cauchy-Riemann system has closed range.
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Szegő kernel asymptotics and Kodaira embedding theorems of Levi-flat CR manifolds [PDF]

Mathematical Research Letters, 2017
Let $X$ be an orientable compact Levi-flat CR manifold and let $L$ be a positive CR complex line bundle over $X$. We prove that certain microlocal conjugations of the associated Szegő kernel admits an asymptotic expansion with respect to high powers of $L$.
Hsiao, Chin-Yu, Marinescu, George
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Classification of Four-Dimensional CR Submanifolds of the Homogenous Nearly Kähler ${\mathbb{S}}^{\mathbf{3}}\mathbf{\times }{\mathbb{S}}^{\mathbf{3}}$ Which Almost Complex Distribution Is Almost Product Orthogonal on Itself

Mathematics
The product manifold S3×S3, which belongs to the homogenous six-dimensional nearly Kähler manifolds, admits two structures, the almost complex structure J and the almost product structure P.
Nataša Djurdjević
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Erratum to: The range of the tangential Cauchy–Riemann system to a CR embedded manifold [PDF]

Inventiones mathematicae, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A remark on the global embedding problem for three-dimensional CR manifolds [PDF]

Proceedings of the American Mathematical Society, 1988
Examples are constructed of compact strictly pseudoconvex real analytic three-dimensional CR manifolds which admit no nonconstant CR functions. Also, the embedding problem for certain CR manifolds is shown to be related to a result of Hadamard on immersed convex hypersurfaces in
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Szegő kernel asymptotics for high power of CR line bundles and Kodaira embedding theorems on CR manifolds [PDF]

Memoirs of the American Mathematical Society, 2018
Let X X be an abstract not necessarily compact orientable CR manifold of dimension
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Szegő kernel expansion and equivariant embedding of CR manifolds with circle action

Annals of Global Analysis and Geometry, 2017
Let $X$ be a compact strongly pseudoconvex CR manifold with a transversal CR $S^1$-action. In this paper, we establish the asymptotic expansion of Szegő kernels of positive Fourier components and by using the asymptotics, we show that $X$ can be equivariant CR embedded into some $\mathbb C^N$ equipped with a simple $S^1$-action.
Herrmann, Hendrik, Hsiao, Chin-Yu, Li, Xiaoshan   +2 more
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Equivariant embeddings of strongly pseudoconvex CR manifolds

, 2020
Ich untersuche CR Mannigfaltigkeiten mit eigentlichen, transversalen Gruppenwirkungen. Zuerst zeige ich, dass sich solche Mannigfaltigkeiten immer äquivariant in eine komplexe Mannigfaltigkeit mit holomorpher Gruppenwirkung einbetten lassen. Dies nutze ich, um zu beweisen, dass der Quotient nach der Wirkung immer die Struktur eines komplexen Raumes ...
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CR regular embeddings and immersions of compact orientable 4-manifolds into ℂ³ [PDF]

International Journal of Mathematics, 2015
We show that a compact orientable 4-manifold M has a CR regular immersion into ℂ3 if and only if both its first Pontryagin class p1(M) and its Euler characteristic χ(M) vanish, and has a CR regular embedding into ℂ3 if and only if in addition the second Stiefel–Whitney class w2(M) vanishes.
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On Convergent Poincaré-Moser Reduction for Levi Degenerate Embedded $5$-Dimensional CR Manifolds

, 2020
References ...
Foo, Wei-Guo, Merker, Joël, Ta, The-Anh
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