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http://dx.doi.org/10.4134/BKMS.b210904

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.6, 2022 , pp. 1567-1594 More about this Journal
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
Nearly Kahler ${\mathbb{S}}^3\; {\times}\; {\mathbb{S}}^3$; Hopf hypersurface; commuting Ricci tensor; pseudo-anti commuting Ricci tensor; Ricci soliton;
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