In this paper, we discuss the Weyl problem in warped product spaces. We apply the method of continuity and prove the openness
of the Weyl problem. A counterexample is constructed to show that the isometric embedding of the sphere with canonical metric
is not unique up to an isometry if the ambient warped product space is not a space form. Then, we study the rigidity of the
standard sphere if we fi x its geometric center in the ambient space. Finally, we discuss a Shi-Tam type of inequality for the
Schwarzschild manifold as an application of our findings.