On the convexity of the Kobayashi metric on a taut complex manifold
Let \(M\) be an \(m\)-dimensional complex manifold, and \(F_M\) be the Kobayashi-Royden pseudo-metric on \(M\). \(F_M\) induces a pseudo-distance \(d_M\), which is called the Kobayashi pseudo-distance. \textit{S. Kobayashi} recently introduced [Int. J. Math. 1, 83-90 (1990; Zbl 0702.32021)] a new infinitesimal pseudo-metric \({\hat F}_M\) on \(M\) which is the double dual of \(F_M\). This paper proves that, if \(M\) is a taut complex manifold, then \({\mathcal D}d_M\) exists, and \({\mathcal D}d_M={\hat F}_M\), where \({\mathcal D}d_M\) is the \textit{derivative} of \(d_M\) (see the paper for the precise definition).
scientific article; zbMATH DE number 1537830