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HOPF HYPERSURFACES OF THE HOMOGENEOUS NEARLY KÄHLER 𝕊3 × 𝕊3 SATISFYING CERTAIN COMMUTING CONDITIONS

  • Xiaomin, Chen (College of Science China University of Petroleum-Beijing) ;
  • Yifan, Yang (College of Science China University of Petroleum-Beijing)
  • Received : 2021.12.16
  • Accepted : 2022.05.02
  • Published : 2022.11.30

Abstract

In this article, we first introduce the notion of commuting Ricci tensor and pseudo-anti commuting Ricci tensor for Hopf hypersurfaces in the homogeneous nearly Kähler 𝕊3 × 𝕊3 and prove that the mean curvature of hypersurface is constant under certain assumptions. Next, we prove the nonexistence of Ricci soliton on Hopf hypersurface with potential Reeb vector field, which improves a result of Hu et al. on the nonexistence of Einstein Hopf hypersurfaces in the homogeneous nearly Kähler 𝕊3 × 𝕊3.

Keywords

Acknowledgement

This research was supported by Science Foundation of China University of Petroleum-Beijing (Nos. 2462020XKJS02, 2462020YXZZ004). The first author expresses thanks to China Scholarship Council for supporting him to visit University of Turin and expresses his gratitude to Professor Luigi Vezzoni and Department of Mathematics for their hospitality. The authors also would like to thank the referee for the valuable comments on this paper.

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