Hyper-Kähler sigma models on (co)tangent bundles with SO(n) isometry

We construct N=2 supersymmetric nonlinear sigma models whose target spaces are tangent as well as cotangent bundles over the quadric surface Qn−2=SO(n)/[SO(n−2)×U(1)]. We use the projective superspace framework, which is an off-shell formalism of N=2 supersymmetry.