  Symmetry algebras of Killing vector fields and conformal Killing vectors
fields can be extended to Killing-Yano and conformal Killing-Yano superalgebras
in constant curvature manifolds. By defining $\mathbb{Z}$-gradations and
filtrations of these superalgebras, we show that the second cohomology groups
of them are trivial and they cannot be deformed to other Lie superalgebras.
This shows the rigidity of Killing-Yano and conformal Killing-Yano
superalgebras and reveals the fact that they correspond to geometric invariants
of constant curvature manifolds. We discuss the structures and dimensions of
these superalgebras on $AdS$ spacetimes as examples.
