2024 : 11 : 13
Firooz Pashaie

Firooz Pashaie

Academic rank: Associate Professor
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Education: PhD.
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Research

Title
On C-biconservative hypersurfaces hypersurfgaces of non-flat Riemannian 4-space forms
Type
JournalPaper
Keywords
Cheng-Yau operator, C-biconservative, scalar curvature.
Year
2024
Journal Honam Mathematical Journal
DOI
Researchers Firooz Pashaie

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 : M^3 → M^4(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.