Firooz Pashaie - Department of Mathematics, Faculty of Basic Sciences, University of Maragheh, Maragheh, Iran

In this manuscript, we consider an extended version of biconservativity condition (namely, {\textrm C}-biconservativity) on the Riemannian hypersurfaces of Lorentzian standard ۴-space forms. This new condition is obtained by substituting the Cheng-Yau operator {\textrm C} instead of the Laplace operator \Delta. We show that every {\textrm C}-biconservative Riemannian hypersurface of a Lorentzian ۴-space form with constant mean curvature has constant scalar curvature.

Cheng-Yau operator, {\textrm C}-biconservative, scalar curvature