Rigidity of the almost complex surfaces in the nearly Kähler

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• 作者：Zejun Hu ^{huzj@zzu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yinshan Zhang ; ^{zhangysookk@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53C24 ; 53C42
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：100
• 期：Complete
• 页码：80-91
• 全文大小：411 K

文摘

In this paper we first show that the well-known nearly Kähler manifold class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044015002454&_mathId=si1.gif&_user=111111111&_pii=S0393044015002454&_rdoc=1&_issn=03930440&md5=242369bf130fbf55b58e510aea79aac8" title="Click to view the MathML source">S³×S³class="mathContainer hidden">class="mathCode">${\mathbb{S}}^3\times {\mathbb{S}}^3$ is neither locally symmetric nor Chern flat. Then, by studying the rigidity of compact almost complex surfaces in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044015002454&_mathId=si1.gif&_user=111111111&_pii=S0393044015002454&_rdoc=1&_issn=03930440&md5=242369bf130fbf55b58e510aea79aac8" title="Click to view the MathML source">S³×S³class="mathContainer hidden">class="mathCode">${\mathbb{S}}^3\times {\mathbb{S}}^3$, we establish a Simons’ type integral inequality so that we obtain a new characterization of two typical examples of totally geodesic almost complex surfaces in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044015002454&_mathId=si1.gif&_user=111111111&_pii=S0393044015002454&_rdoc=1&_issn=03930440&md5=242369bf130fbf55b58e510aea79aac8" title="Click to view the MathML source">S³×S³class="mathContainer hidden">class="mathCode">${\mathbb{S}}^3\times {\mathbb{S}}^3$.