Laplacian Conditions and Sphericity of Hypersurfaces in the Nearly Kähler 6-Sphere

Ibrahim Al-Dayel ()
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Ibrahim Al-Dayel: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box-65892, Riyadh 11566, Saudi Arabia

Mathematics, 2025, vol. 13, issue 16, 1-9

Abstract: In this paper, we investigate hypersurfaces in the nearly Kähler 6-sphere S 6 and establish several foundational results. In particular, under certain conditions of the function ξ ( f ) = g ( ∇ f , ξ ) , we demonstrate that a hypersurface M of S 6 must be a sphere. Here, f ∈ C ∞ ( M ) is a smooth vector field, ξ = − J N denotes the characteristic vector field, J is the almost complex structure on S 6 , and N is the unit vector field normal to the hypersurface. We also support our results with illustrative examples.

Keywords: hypersurfaces; Ricci curvature; nearly Kähler 6-sphere (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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