TY - JOUR
AU - Barboza, Weiller F. C.
AU - de Lima, Henrique F.
AU - Velásquez, Marco Antonio L.
PY - 2022/12/04
Y2 - 2023/09/27
TI - Gap type results for spacelike submanifolds with parallel mean curvature vector
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 128
IS - 3
SE - Articles
DO - 10.7146/math.scand.a-133368
UR - https://www.mscand.dk/article/view/133368
SP -
AB - <p>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 $\mathbb L_q^{n+p}(c)$ of index $1\leq q\leq p$ and constant sectional curvature $c\in \{-1,0,1\}$. 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).</p>
ER -