## Journal of Mathematics of Kyoto University

### Holomorphic $\mathbb{C}$-fibrations and pseudoconvexity of general order

#### Abstract

We consider a domain $D$ in $\mathbb{C}^{n}$ such that there is a Stein manifold $E$ which is a $\mathbb{C}$-fibration over $D$. Simple examples show that $D$ does not need to be Stein. However it cannot be arbitrarily and, in fact, we prove that $D$ is pseudoconvex of order $n-2$.

#### Article information

Source
J. Math. Kyoto Univ., Volume 46, Number 4 (2006), 693-700.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281599

Digital Object Identifier
doi:10.1215/kjm/1250281599

Mathematical Reviews number (MathSciNet)
MR2320346

Zentralblatt MATH identifier
1138.32005

Subjects
Primary: 32F10: $q$-convexity, $q$-concavity
Secondary: 32E10: Stein spaces, Stein manifolds 32F17: Other notions of convexity

#### Citation

Tomassini, Giuseppe; Vâjâitu, Viorel. Holomorphic $\mathbb{C}$-fibrations and pseudoconvexity of general order. J. Math. Kyoto Univ. 46 (2006), no. 4, 693--700. doi:10.1215/kjm/1250281599. https://projecteuclid.org/euclid.kjm/1250281599