Einige Kennzeichnungen der homothetischen Abbildungen eines Riemannschen Raumes unter den kreistreuen Abbildungen

Abstract

In a previous note the author has shown that each circular mapping of a Riemannian manifold is a conformal mapping. Circular mappings therefore are situated between the conformal and the homothetic mappings. In the following paper some local and global theorems are proved characterizing homothetic mappings among the circular mappings. For example: Let Vn,\(\bar V^n \) be complete Riemannian manifolds and let f:\(V^n \to \bar V^n \) be a circular mapping, which transforms a single geodesic triangle of Vn into a geodesic triangle of\(\bar V^n \). Then f is a homothetic mapping.