Kobayashi-Royden vs. Hahn pseudometric in ${\Bbb C}^2$

Details Kobayashi-Royden vs. Hahn pseudometric in ${\Bbb C}^2$ Kobayashi-Royden vs. Hahn pseudometric in ${\Bbb C}^2$

2000-09-25

arxiv.org/abs/math/0009215v2

Ann. Polon. Math. 75 (2000), 289-294.

Mathematics

Complex Variables

5 pages

Scientific paper

For a domain $D\subset{\Bbb C}$ the Kobayashi--Royden $\kappa$ and Hahn $h$ pseudometrics are equal iff $D$ is simply connected. Overholt showed that for $D\subset{\Bbb C}^n$, $n\geq3$, we have $h_D\equiv\kappa_D$. Let $D_1,D_2\subset{\Bbb C}$. The aim of this paper is to show that $h_{D_1\times D_2}\equiv\kappa_{D_1\times D_2}$ iff at least one of $D_1$, $D_2$ is simply connected or biholomorphic to ${\Bbb C}\setminus\{0\}$. In particular, there are domains $D\subset{\Bbb C}^2$ for which $h_D\not\equiv\kappa_D$.

Affiliated with

Also associated with

No associations

Rating

Kobayashi-Royden vs. Hahn pseudometric in ${\Bbb C}^2$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Kobayashi-Royden vs. Hahn pseudometric in ${\Bbb C}^2$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Kobayashi-Royden vs. Hahn pseudometric in ${\Bbb C}^2$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-605641