On $OSp(N\mathrm{\mid }2)$ superconformal mechanics

Superparticle models with $OSp(N\mathrm{\mid }2)$ supersymmetry group are studied. We first consider the $N=4$ case and construct the models with $\kappa$-symmetry on the coset spaces of the $OSp(4\mathrm{\mid }2)$ supergroup. In addition, within the canonical formalism we present an $OSp(4\mathrm{\mid }2)$ superparticle model with semi-dynamical angular variables. For generic $N$ we construct a superparticle model on $Ad{S}_2\times S^{N-1}$ with the reduced $\kappa$-symmetry. It is demonstrated that the Hamiltonian of this model has the same structure as the one for the $N=4$ case because additional fermions contribute to the second-class constraints only.