호남수학학술지 (Honam Mathematical Journal)

  • 제46권2호
  • /
  • Pages.237-248
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  • 2024
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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ON C-BICONSERVATIVE HYPERSURFACES OF NON-FLAT RIEMANNIAN 4-SPACE FORMS

  • Firooz Pashaie (Department of Mathematics, University of Maragheh)
  • 투고 : 2023.08.20
  • 심사 : 2023.11.23
  • 발행 : 2024.06.25
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초록

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.

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과제정보

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

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