(untitled) (Journal of Mathematical Study, 2023)
Assume that M^n(n≥3) is a complete hypersurface in R^n+1 with zero scalar curvature. Assume that B, H, g is the second fundamental form, the mean curvature and the induced metric of M, respectively. We prove that M is a hyperplane if -P_1( abla H, abla|H|)≤-δ|H|| abla H|^2 for some positive constant δ, where P_1=nHg-B which denotes the first order Newton transformation, and (_M|H|^ndv)^1n