We show in this paper that every domain in a separable Hilbert space, say H, which has a C smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of H. This is the complete generalization of the Wong-Rosay theorem to a separable Hilbert space of infinite dimension. Our work here is an improvement from the preceding work of Kim/Kr...

We derive a local ansatz for generalized K\"ahler surfaces with nondegenerate Poisson structure and biholomorphic $S^1$ action which generalizes the classic Gibbons-Hawking invariant hyperK\"ahler manifolds, allows choice of one arbitrary function. By imposing K\"ahler-Ricci soliton equation, or equivalently equations type IIB string theory, construction becomes rigid, we classify all complete ...