Abstract:
We consider the linear Weingarten
spacelike submanifold
immersed in semi-Riemannian space
form
$\mathbb {N}^{n+p} _q (c)$
of
constant sectional curvature
$c$
and index
$q$,
where
$p \ge q>1$.
In this paper,
our approach involves an
appropriately generalized
maximum principle for a
suitable Cheng–Yau
modified operator so as to
obtain that the submanifold
is definitely either totally umbilical
or isometric to a product space.
