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

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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)

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.

Suggested Citation

  • Ibrahim Al-Dayel, 2025. "Laplacian Conditions and Sphericity of Hypersurfaces in the Nearly Kähler 6-Sphere," Mathematics, MDPI, vol. 13(16), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2673-:d:1728228
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