Any Sasakian structure is approximated by embeddings into spheres

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-08-07 DOI:10.1515/forum-2023-0364

Andrea Loi, Giovanni Placini

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引用次数: 0

Abstract

We show that, for any given q ≥ 0

{q\geq 0}

, any Sasakian structure on a closed manifold M is approximated in the C q

{C^{{q}}}

-norm by structures induced by CR embeddings into weighted Sasakian spheres. In order to obtain this result, we also strengthen the approximation of an orbifold Kähler form by projectively induced ones given in [J. Ross and R. Thomas, Weighted projective embeddings, stability of orbifolds, and constant scalar curvature Kähler metrics, J. Differential Geom. 88 2011, 1, 109–159] in the C 0

{C^{0}}

-norm to a C q

{C^{{q}}}

-approximation.

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任何萨萨基结构都可以通过嵌入球面来近似

我们证明，对于任何给定的 q ≥ 0 {q\geq 0}，闭流形 M 上的任何萨萨基结构在 C q {C^{{q}} 中都是近似的。｝ -的结构近似。为了得到这个结果，我们还加强了 [J. Ross and R. Thomas, Weighted Sasakian spheres] 中给出的用投影诱导的球面凯勒形式对球面凯勒形式的逼近。Ross and R. Thomas, Weighted projective embeddings, stability of orbifolds, and constant scalar curvature Kähler metrics, J. Differential Geom.88 2011, 1, 109-159] 中的 C 0 {C^{0}} -norm。 -C q {C^{{q}} 的近似。｝ -的近似。

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.