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Article Dans Une Revue Differential Geometry and its Applications Année : 2021

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

Zejun Hu
  • Fonction : Auteur
Marilena Moruz
  • Fonction : Auteur
Zeke Yao
  • Fonction : Auteur

Résumé

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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Dates et versions

hal-03722556 , version 1 (13-07-2022)

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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, 2021, 75, pp.101717. ⟨10.1016/j.difgeo.2021.101717⟩. ⟨hal-03722556⟩
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