Integrable Generators of Lie Algebras of Vector Fields on the Koras--Russell Cubic Threefold

Abstract

The Koras--Russell cubic threefold is a complex-affine manifold that is diffeomorphic to the three-dimensional complex-Euclidean space, but not algebraically isomorphic to the three-dimensional complex-affine space as an affine variety. We study the Lie algebra of polynomial vector fields on the Koras--Russell cubic threefold; We prove that the compositions of the flows of a list of complete vector fields approximate every holomorphic automorphism that is in the path-connected component of the identity.