  The classical Minkowski formula is extended to spacelike codimension-two
submanifolds in spacetimes which admit "hidden symmetry" from conformal
Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem
for spacelike codimension-two submanifolds in a static spherically symmetric
spacetime: a codimension-two submanifold with constant normalized null
expansion (null mean curvature) must lie in a shear-free (umbilical) null
hypersurface. These results are generalized for higher order curvature
invariants. In particular, the notion of mixed higher order mean curvature is
introduced to highlight the special null geometry of the submanifold. Finally,
Alexandrov type theorems are established for spacelike submanifolds with
constant mixed higher order mean curvature, which are generalizations of
hypersurfaces of constant Weingarten curvature in the Euclidean space.
