Warped Product Semi-Invariant Submanifolds in Almost Paracontact Riemannian Manifolds

Abstract EN

We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively.

Therefore, we consider warped product semi-invariant submanifolds in the form N=N⊥×fNT by reversing two factor manifolds NT and N⊥.

We prove several fundamental properties of warped product semi-invariant submanifolds in an almost paracontact Riemannian manifold and establish a general inequality for an arbitrary warped product semi-invariant submanifold.

After then, we investigate warped product semi-invariant submanifolds in a general almost paracontact Riemannian manifold which satisfy the equality case of the inequality.