A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms

Abstract

The aim of this paper is to study the invariant submanifolds of a $(\kappa, \mu)$-paracontact metric space form. We characterize $(\kappa,\mu)$-paracontact metric space form satisfying the curvature conditions $\nabla\sigma$=0, $R\cdot{\sigma}=0$, $R\cdot{\nabla\sigma}=0$ and $\widetilde{C}\cdot\sigma=0$. Finally, we see that these conditions are equivalent to $\sigma=0$.