部分可积的几乎CR结构

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2021-01-01 DOI:10.1515/coma-2020-0124

T. Akahori

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引用次数: 0

摘要

摘要设（M，D）是一个dimRM=2n≥5的紧致接触流形。这意味着：M是一个具有dimRM=2n≥5的C∞微分流形。D是切丛TM的一个子丛，满足；存在一个实的形式θ，使得D＝{X:X∈TM，θ（X）＝0}，并且在M的每个p点θ^∧n−1（D）≠0。特别地，我们假设我们的D几乎允许CR结构，（M，S）。本文受Matsumoto（[M]）工作的启发，研究了部分可积几乎CR结构与实际CR结构的区别。并从CR结构的变形理论（[A1]，[AGL]）的角度讨论了部分可积的几乎CR结构。

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Partially integrable almost CR structures

Abstract Let (M, D) be a compact contact manifold with dimRM = 2n ≥ 5. This means that: M is a C∞ differential manifold with dimRM = 2n ≥ 5. And D is a subbundle of the tangent bundle TM which satisfying; there is a real one form θ such that D = {X : X ∈ TM, θ(X) = 0}, and θ ^ Λn−1(d ) ≠ 0 at every point of p of M. Especially, we assume that our D admits almost CR structure,(M, S). In this paper, inspired by the work of Matsumoto([M]), we study the difference of partially integrable almost CR structures from actual CR structures. And we discuss partially integrable almost CR structures from the point of view of the deformation theory of CR structures ([A1],[AGL]).

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.