Strongly pseudoconvex homogeneous domains in almost complex manifolds

Lee, Kang-Hyurk

doi:10.1515/crelle.2008.074

Cited by 10 publications

(14 citation statements)

References 8 publications

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“…In this section, we would like to recapitulate the contents of [14] pertaining to the model domains.…”

Section: Lee Modelsmentioning

confidence: 99%

On the Differential Geometric Characterization of The Lee Models

Choi

2010

J Geom Anal

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This paper pertains to the J -Hermitian geometry of model domains introduced by Lee (Mich. We first construct a Hermitian invariant metric on the Lee model and show that the invariant metric actually coincides with the Kobayashi-Royden metric, thus demonstrating an uncommon phenomenon that the Kobayashi-Royden metric is J -Hermitian in this case. Then we follow Cartan's differential-form approach and find differential-geometric invariants, including torsion invariants, of the Lee model equipped with this J -Hermitian Kobayashi-Royden metric, and present a theorem that characterizes the Lee model by those invariants, up to J -holomorphic isometric equivalence. We also present an all dimensional analysis of the asymptotic behavior of the Kobayashi metric near the strongly pseudoconvex boundary points of domains in almost complex manifolds.

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“…In this section, we would like to recapitulate the contents of [14] pertaining to the model domains.…”

Section: Lee Modelsmentioning

confidence: 99%

On the Differential Geometric Characterization of The Lee Models

Choi

2010

J Geom Anal

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“…. , z n ) is an example of strongly pseudoconvex domain which is homogeneous but not biholomorphic to the complex Euclidean ball with the standard complex structure (see [12,13]). It contrasts to the Wong-Rosay theorem which states that the complex Euclidean ball is only a homogeneous domain with a strongly pseudoconvex boundary in a complex manifold ( [2]).…”

Section: Definition 34mentioning

confidence: 99%

“…For the cases n = m − 1 we present in Theorems 2.10 and 2.11 a necessary and sufficient condition for (M, J ) to admit a complex submanifold N of complex dimension n. Our viewpoint is purely local: On a neighborhood of a reference point P ∈ M we investigate the rank condition of the torsion tensor as in (2.4) or (2.10) and then we use the Newlander-Nirenberg theorem. This paper has been motivated by the second author's thesis ( [12,13]) where he discusses a model almost complex structure obtained by perturbing the standard complex structure by linear functions. H. Gaussier and A. Sukhov studied the same model structure in [4].…”

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confidence: 99%

Integrable Submanifolds in Almost Complex Manifolds

Han

Lee

2009

J Geom Anal

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Let (M, J ) be a germ of an almost complex manifold of real dimension 2m and let n (n < m) be an integer. We study a necessary and sufficient condition for M to admit an integrable submanifold N of complex dimension n. If n = m − 1, we find defining functions of N explicitly from the coefficients of the torsion tensor. For J obtained by small perturbation of the standard complex structure of C m this condition is given as an overdetermined system of second order PDEs on the perturbation. The proof is based on the rank conditions of the Nijenhuis tensor and application of the Newlander-Nirenberg theorem. We give examples of almost complex structures on C 3 : the ones with a single complex submanifold of dimension 2 and the ones with 1-parameter or 2-parameter families of complex submanifolds of dimension 2.

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“…It plays as a model in the study of strongly pseudoconvex domains in almost complex manifolds. Moreover, the Siegel half space with a model structure is an example of strongly pseudoconvex domain which is homogeneous but not biholomorphic to the complex Euclidean ball endowed with the standard structure by the non-integrability (see [11,12]). It contrasts to the Wong-Rosay theorem: the complex Euclidean ball is only a homogeneous domain with a strongly pseudoconvex boundary in a complex manifold up to the biholomorphic equivalence (see [3]).…”

Section: Non-integrable Almost Complex Structures With Infinite Dimenmentioning

confidence: 99%

“…It contrasts to the Wong-Rosay theorem: the complex Euclidean ball is only a homogeneous domain with a strongly pseudoconvex boundary in a complex manifold up to the biholomorphic equivalence (see [3]). Now we introduce model structures as in [12]. Let B = (B jk ) j,k=2,...,n be a complex, skew-symmetric (n − 1) × (n − 1) matrix.…”

Section: Non-integrable Almost Complex Structures With Infinite Dimenmentioning

confidence: 99%

Complete prolongation for infinitesimal automorphisms on almost complex manifolds

Kim

Lee

2009

Math. Z.

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We study the almost complex manifold and its symmetry algebra, the set of germs of infinitesimal automorphisms. The main result is that there is a certain condition to a torsion bundle under which the dimension of the symmetry algebra can not exceed 4 in the case of complex dimension 2. We will give an example which attains the maximal dimension 4, and another example without non-degeneracy whose symmetry algebra is of infinite dimension.

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Strongly pseudoconvex homogeneous domains in almost complex manifolds

Cited by 10 publications

References 8 publications

On the Differential Geometric Characterization of The Lee Models

On the Differential Geometric Characterization of The Lee Models

Integrable Submanifolds in Almost Complex Manifolds

Complete prolongation for infinitesimal automorphisms on almost complex manifolds

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