On conformal equivalence of Berwald manifolds all of whose indicatrices have positive curvature

Abstract

The problem given by M. Matsumoto in his paper [10] is that whether there exist conformally equivalent Berwald, or locally Minkowski manifolds. In this paper we are interested in case of positive definite Berwald manifolds of dimension $n\ge 3$ solving the problem under a further condition: we shall suppose that one, and therefore all indicatrices have positive curvature. Then the conformal change must be homothetic unless the Berwald manifolds are Riemannian.