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On the nonexistence and rigidity for hypersurfaces of the homogeneous nearly Kähler S3×S3

Abstract : In this paper, we study hypersurfaces of the homogeneous NK (nearly Kähler) manifold S3×S3. As the main results, we first show that the homogeneous NK S3×S3 admits neither locally conformally flat hypersurfaces nor Einstein Hopf hypersurfaces. Then, we establish a Simons type integral inequality for compact minimal hypersurfaces of the homogeneous NK S3×S3 and, as its direct consequence, we obtain new characterizations for hypersurfaces of the homogeneous NK S3×S3 whose shape operator A and induced almost contact structure ϕ satisfy Aϕ=ϕA. Hypersurfaces of the NK S3×S3 satisfying this latter condition have been classified in our previous joint work (Hu et al. 2018 [18])
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Submitted on : Wednesday, July 13, 2022 - 2:45:10 PM
Last modification on : Thursday, July 14, 2022 - 3:55:32 AM

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Zejun Hu, Marilena Moruz, Luc Vrancken, Zeke Yao. On the nonexistence and rigidity for hypersurfaces of the homogeneous nearly Kähler S3×S3. Differential Geometry and its Applications, Elsevier, 2021, 75, pp.101717. ⟨10.1016/j.difgeo.2021.101717⟩. ⟨hal-03722556⟩

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