Abstract
Let $X$ be a n-dimensional Stein (connected complex) manifold or a compact one whose universal covering is a domain in $\mathbf{C}^n$ or a Stein manifold. Let $\Delta_X$ be the degeneration locus of Kobayashi pseudodistance of $X$ which is contained in a hypersurface $S$ of $X$. Then $X$ is hyperbolic modulo $S$ and taut modulo $S$.
Highlights
In Kiernan and Kobayashi (1973) the Problem 1 was raised to determine the relationship between “taut mod Δ” and “complete hyperbolic mod Δ” and the Problem 2 asked that “hyperbolically imbedded mod Δ” imply “tautly imbedded mod Δ”.When Δ ∅, these problems are not solved yet
Let X be a n-dimensional Stein manifold or a compact one whose universal covering is a domain in Cn or a Stein manifold
(1) We prove that P = {p0} if P ∅
Summary
Yukinobu Adachi Nishinomiya City, Kurakuen 2-bannchyo, Japan Correspondence: Yukinobu Adachi, Nishinomiya City, Kurakuen 2-bannchyo, Japan. Received: January 14, 2013 Accepted: February 4, 2013 Online Published: March 14, 2013 doi:10.5539/jmr.v5n2p39
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