Kählerian extensions of the symplectic reduction.
We define and investigate the notion of k-convexity in the sense of Mejia-Minda for domains in ℂⁿ and also that of k-convex mappings on the Euclidean unit ball.
For a domain D ⊂ ℂ the Kobayashi-Royden ϰ and Hahn h pseudometrics are equal iff D is simply connected. Overholt showed that for , n ≥ 3, we have . Let D₁, D₂ ⊂ ℂ. The aim of this paper is to show that iff at least one of D₁, D₂ is simply connected or biholomorphic to ℂ 0. In particular, there are domains D ⊂ ℂ² for which .