The ℳ-projective curvature tensor field on generalized (κ,μ)-paracontact metric manifolds

We consider generalized ( κ , μ ) {(\kappa,\mu)} -paracontact metric manifolds satisfying certain flatness conditions on the ℳ {\mathcal{M}} -projective curvature tensor. Specifically, we study ξ- ℳ {\mathcal{M}} -projectively flat and ℳ {\mathcal{M}} -projectively flat generalized ( κ , μ ) {(\kappa,\mu)} -paracontact metric manifolds and, further, ϕ- ℳ {\mathcal{M}} -projectively symmetric generalized ( κ ≠ - 1 , μ ) {(\kappa\neq-1,\mu)} -paracontact metric manifolds. We prove that they are characterized by certain structures whose properties are discussed in some detail.