Twistor geometry for hyperkähler metrics on complex adjoint orbits (Q1370910)

The author proposes a twistor approach for constructing hyperkähler metrics on complex semisimple adjoint orbits motivated by works of \textit{D. Burns} [Aspects Math. E9, 51-67 (1986; Zbl 0596.53057)] and \textit{P. B. Kronheimer} [J. Lond. Math. Soc., II. Ser. 42, 193-208 (1990; Zbl 0721.22006)]. He defines the twistor space as the union of certain regular adjoint orbits and exhibits a family of twistor lines. He also gives an algebraic characterization of the twistor lines. Finally, he discusses a construction of hyperkähler metrics by means of the identification, at least locally, of an adjoint orbit with the parameter space of twistor lines of its twistor space.