The Levi problem for a product manifold

Yasou Matsugu

Vol. 46 (1973), No. 1, 231–233

DOI: 10.2140/pjm.1973.46.231

Abstract

Let S be a Stein manifold, T a one dimensional torus, π a projection of the product E = S × T onto S and D a subdomain of E. The main object of this paper is to prove that D is a Stein manifold if and only if D is pseudoconvex in the sense of Cartan and π⁻¹(x) is not contained in D for any point x of S.

Mathematical Subject Classification 2000

Primary: 32F15

Secondary: 32E10

Milestones

Received: 1 February 1972

Published: 1 May 1973