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

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 -> M 4 ( c ) is said to be biconservative if it satisfies the equation (triangle 2x)inverted perpendicular = 0, where triangle is the Laplace operator on M3 and inverted perpendicular 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 triangle. We prove that C-biconservative hypersurfaces of Riemannian 4-space forms (with some additional conditions) have constant scalar curvature.