Gap type results for spacelike submanifolds with parallel mean curvature vector - Barboza, Weiller F. C.; de Lima, Henrique F.; Velásquez, Marco Antonio L. (MATHEMATICA SCANDINAVICA, 2022)
We deal with n-dimensional spacelike submanifolds immersed with parallel mean curvature vector (which is supposed to be either spacelike or timelike) in a pseudo-Riemannian space form L_q^n+p(c) of index 1≤ q≤ p and constant sectional curvature c{-1,0,1}. Under suitable constraints on the traceless second fundamental form, we adapt the technique developed by Yang and Li (Math. Notes 100 (2016) 298–308) to prove that such a spacelike submanifold must be totally umbilical. For this, we apply a maximum principle for complete noncompact Riemannian manifolds having polynomial volume growth, recently established by Alías, Caminha and Nascimento (Ann. Mat. Pura Appl. 200 (2021) 1637–1650).