A classification of submanifolds of (κ, µ)-paracontact metric space forms

The aim of this paper is to study the invariant submanifolds of a (κ, µ)-paracontact metric space form. We characterize (κ, µ)-paracontact metric space form satisfying the curvature conditions ∇σ=0, R · σ = 0, R · ∇σ = 0 and ˜C · σ = 0. Finally, we see that these conditions are equivalent to σ = 0.