MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X$ be a complex manifold, let $\Omega \subseteq {\bf C} \times X$ be defined by $\Omega = \{ (z,p) \in {\bf C} \times X : a(p) < Im z < - b(p) \} $ where $a$ and $b$ are plurisubharmonic functions on $X$ with $a + b < 0.$ Assume that $\Omega$ is a Stein manifold, is it true that $X$ is a Stein manifold ? If with the same assumtpion we suppose that $X$ is locally eucledean countable basis "complex manifold" but not in general Hausdorff, can we conclude that $X$ must be Hausdorff ? This question is related to the possibility to embedding a manifold with the holomorphic action of a real Lie group into some space where there is an action of the complexified group.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.