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"> 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">, 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">.