Honam Mathematical Journal (호남수학학술지)

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ON C-BICONSERVATIVE HYPERSURFACES OF NON-FLAT RIEMANNIAN 4-SPACE FORMS

  • Received : 2023.08.20
  • Accepted : 2023.11.23
  • Published : 2024.06.25
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Abstract

In this manuscript, the hypersurfaces of non-flat Riemannian 4-space forms are considered. A hypersurface of a 4-dimensional Riemannian space form defined by an isometric immersion 𝐱 : M3 → 𝕄4(c) is said to be biconservative if it satisfies the equation (∆2𝐱 )⊤ = 0, where ∆ is the Laplace operator on M3 and ⊤ stands for the tangent component of vectors. We study an extended version of biconservativity condition on the hypersurfaces of the Riemannian standard 4-space forms. The C-biconservativity condition is obtained by substituting the Cheng-Yau operator C instead of ∆. We prove that C-biconservative hypersurfaces of Riemannian 4-space forms (with some additional conditions) have constant scalar curvature.

Keywords

Acknowledgement

The author is grateful to the anonymous reviewers for their careful reading of the paper and their suggestions and corrections.

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