Warped Product Submanifolds of Riemannian Product Manifolds

Abstract

We study warped product of the type $N_{\theta }{\times }_f{N}_T$ and $N_{\theta }{\times }_f{N}_{\perp }$, where $N_{\theta }$, $N_T$, and $N_{\perp }$ are proper slant, invariant, and anti-invariant submanifolds, respectively, and we prove some basic results and finally obtain some inequalities for squared norm of second fundamental form.