Orthogonal almost complex structure and its Nijenhuis tensor

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-03-05 DOI:10.1112/blms.70044

Zizhou Tang, Wenjiao Yan

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引用次数: 0

Abstract

In this paper, we demonstrate that on an almost Hermitian manifold $(M^{2 n}, J, d s^{2})$ , a 2-form $φ = S^{*} Φ$ , the pullback of the Kähler form $Φ$ on the twistor bundle over $M^{2 n}$ , is nondegenerate if the squared norm ${| N |}^{2}$ of the Nijenhuis tensor is less than $\frac{64}{5}$ when $n ⩾ 3$ or less than 16 when $n = 2$ . As one of the consequences, there exists no orthogonal almost complex structure on the standard sphere $(S^{6}, d s_{0}^{2})$ with ${| N |}^{2} < \frac{64}{5}$ everywhere.

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正交几乎复结构及其Nijenhuis张量

在本文中，我们证明了在一个几乎厄米流形（m2n， J, ds2） $(M^{2n}, J, ds^2)$上，a 2-form φ = S∗Φ $\varphi =S^*\Phi$；在m2n $M^{2n}$上，Kähler形式Φ $\Phi$对扭束的回拉，是非简并的如果Nijenhuis张量的平方范数| N | 2 $|N|^2$小于64 5 $\frac{64}{5}$当N大于或等于3$n\geqslant 3$或当n = 2时小于16 $n=2$。作为结果之一，在标准球（s6）上不存在正交的几乎复杂结构。d s 0 2) $(S^6, ds_0^2)$ with | N | 2 ＆lt；64 5 $|N|^2<\frac{64}{5}$到处都是。

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