Kähler具有大对称性的梯度里奇孤子

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-04-03 DOI:10.1016/j.aim.2025.110253

Hung Tran

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引用次数: 0

摘要

设（M,g，J,f）是一个实维2n的不可约非平凡Kähler梯度Ricci孤子。我们证明了它的等距组的维数不超过n2，并刻画了相等的情况。因此，我们的框架证明了先前构造的U(n)-不变Kähler梯度Ricci孤子的唯一性。这里有关于自同构群或仿射变换的推论，也有关于几乎厄密GRS的一般版本。该方法基于与几乎接触的度量结构的几何结构的连接。

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Kähler gradient Ricci solitons with large symmetry

Let

(M, g, J, f)

be an irreducible non-trivial Kähler gradient Ricci soliton of real dimension 2n. We show that its group of isometries is of dimension at most

n^{2}

and the case of equality is characterized. As a consequence, our framework shows the uniqueness of

U (n)

-invariant Kähler gradient Ricci solitons constructed earlier. There are corollaries regarding the groups of automorphisms or affine transformations and a general version for almost Hermitian GRS. The approach is based on a connection to the geometry of an almost contact metric structure.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.