Nearly Kaehler流形$\mathbb{S}$3×$\mathbb{S}$3上的殆切触拉格朗日子流形

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 29-37.

Nearly Kaehler流形 $\mathbb{S}$ ³× $\mathbb{S}$ ³上的殆切触拉格朗日子流形

杨标桂^1,*(),陈静²

¹ 福建师范大学数学与信息学院福州 350117
² 厦门双十中学漳州分校福建漳州 363107

收稿日期:2017-09-26 出版日期:2019-02-26 发布日期:2019-03-12
通讯作者: 杨标桂 E-mail:bgyang@163.com
基金资助:
国家自然科学基金(11761049);福建省自然基金(2016J01004);福建省自然基金(2017J01398)

Almost Contact Lagrangian Submanifolds of Nearly Kaehler $\mathbb{S}$ ³× $\mathbb{S}$ ³

Biaogui Yang^1,*(),Jing Chen²

¹ College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117
² Zhangzhou Branch Compus of Xiamen Shuangshi Middle School, Fujian Zhangzhou 363107

Received:2017-09-26 Online:2019-02-26 Published:2019-03-12
Contact: Biaogui Yang E-mail:bgyang@163.com
Supported by:
国家自然科学基金(11761049);福建省自然基金(2016J01004);福建省自然基金(2017J01398)

摘要/Abstract

摘要：

对于Nearly Kaehler流形 ${\Bbb S}^3\times {\Bbb S}^3$ 上的一个拉格朗日子流形,将给出由 $M$ 上的一个单位向量场典范引出的殆切触度量结构是 $\alpha$ -Sasakian, $\beta$ -Kenmotsu以及cosymplectic的充要条件.另外,当这个殆切触度量结构为正规时,找出在什么条件下这个殆切触度量结构是 $\frac{\sqrt{3}}{3}$ -Sasakian, $\frac{\sqrt{3}}{3}$ -Kenmotsu或cosymplectic结构.

关键词: Nearly Kaehler流形, 拉格朗日子流形, 殆切触度量结构, α-Sasakian结构, β-Kenmotsu结构, Cosymplectic结构

Abstract:

For a Lagrangian submanifold of the nearly Kaehler ${\Bbb S}^3\times {\Bbb S}^3$ , we provide conditions for a canonically induced almost contact metric structure by a unit vector field, to be $\alpha$ -Sasakian, $\beta$ -Kenmotsu and cosymplectic. Furthermore, assuming the almost contact metric structure to be normal, we show the conditions when the contact metric structure is $\frac{\sqrt{3}}{3}$ -Sasakian, $\frac{\sqrt{3}}{3}$ -Kenmotsu or cosymplectic.

Key words: Nearly Kaehler manifold, Lagrangian submanifold, Almost contact metric structure, $\frac{\sqrt{3}}{3}$ -Sasakian structure, $\frac{\sqrt{3}}{3}$ -Kenmotsu structure, Cosymplectic structure

中图分类号:

O186

杨标桂,陈静. Nearly Kaehler流形 $\mathbb{S}$ ³× $\mathbb{S}$ ³上的殆切触拉格朗日子流形[J]. 数学物理学报, 2019, 39(1): 29-37.

Biaogui Yang,Jing Chen. Almost Contact Lagrangian Submanifolds of Nearly Kaehler $\mathbb{S}$ ³× $\mathbb{S}$ ³[J]. Acta mathematica scientia,Series A, 2019, 39(1): 29-37.

参考文献 12

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Nearly Kaehler流形 $\mathbb{S}$ ³× $\mathbb{S}$ ³上的殆切触拉格朗日子流形

Almost Contact Lagrangian Submanifolds of Nearly Kaehler $\mathbb{S}$ ³× $\mathbb{S}$ ³

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