Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (1): 29-37.

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

Biaogui Yang1,*(),Jing Chen2   

  1. 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)

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

CLC Number: 

  • O186
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