Submanifolds with constant scalar curvature in a space form

We deal with complete submanifolds M-n having constant positive scalar curvature and immersed with parallel normalized mean curvature vector field in a Riemannian space form Q(c)(n+P) of constant sectional curvature c is an element of {1, 0, -1}. In this setting, we show that such a submanifold M-n must be either totally umbilical or isometric to a Clifford torus S-1 (root 1 - r(2)) x Sn-1(r), when c = 1, a circular cylinder R x Sn-1(r), when c = 0, or a hyperbolic cylinder H-1 (-root 1 + r(2)) x Sn-1(r), when c = -1. This characterization theorem corresponds to a natural improvement of previous ones due to Alias, Garcia-Martinez and Rigoli [2], Cheng [4] and Guo and Li [6]. (C) 2016 Elsevier Inc. All rights reserved.