Invariant Schwarzian Derivatives of Higher Order

摘要

We derive relations between the Aharonov invariants and Tamanoi's Schwarzian derivatives of higher order and give a recursive formula for Tamanoi's Schwarzians. Then we propose a definition of invariant Schwarzian derivatives of a nonconstant holomorphic map between Riemann surfaces with conformal metrics. We show a recursive formula also for our invariant Schwarzians.