Kähler manifolds have a natural hyperkähler structure associated with (part of) their cotangent bundles. Using projective superspace, we construct four-dimensional N= 2 models on the tangent bundles of some classical Hermitian symmetric spaces (specifically, the four regular series of irreducible compact symmetric Kähler manifolds, and their non-compact versions). A further dualization yields the Kähler potential for the hyperkähler metric on the cotangent bundle.
Ari, M., Kuzenko, S. M., & Lindstrom, U. (2007). Hyperkähler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace. Journal of High Energy Physics, 2007(2), online - approx 5-20pp. https://doi.org/10.1088/1126-6708/2007/02/100