Twisted linear actions on projective spaces (Q910065)

Generalizing \textit{F. Uchida}'s work [Tôhoku Math. J., II. Ser. 39, 61- 69 (1987; Zbl 0622.57028)], the author defines twisted linear actions of Lie groups on complex and quaternionic projective spaces and proves that such actions are equivariantly diffeomorphic to linear actions. Furthermore, there are uncountably many topologically distinct \(C^{\omega}\)-actions of SL(n,\({\mathbb{F}})\) \(({\mathbb{F}}={\mathbb{C}}\) or \({\mathbb{H}})\) on an (nk-1)-dimensional \({\mathbb{F}}\)-projective space when \(n>k\geq 2\). In contrast, there are uncountably many actions which are topologically equivalent but \(C^ 1\)-differentiably distinct.