Abstract
The main objective of this paper is to study the warped product pointwise semi-slant submanifolds which are isometrically immersed into Sasakian manifolds. First, we prove some characterizations results in terms of the shape operator, under which influence a pointwise semi-slant submanifold of a Sasakian manifold can be reduced to a warped product submanifold. Then, we determine a geometric inequality for the second fundamental form regarding to intrinsic invariant and extrinsic invariant using the Gauss equation instead of the Codazzi equation. Evenmore, we give some applications of this inequality into Sasakian space forms, and we will investigate the status of equalities in the inequality. As a particular case, we provide numerous applications of the Green lemma, the Laplacian of warped functions and some partial differential equations. Some triviality results for connected, compact warped product pointwise semi-slant submanifolds of Sasakian space form by means of Hamiltonian and the kinetic energy of warped function involving boundary conditions are established.