The Axiom of Plane on Warped Product Models and Its Application

Abstract

Abstract.We establish the axiom of plane for warped product models. The axiom applies to a classical problem discussed by H. von Mangoldt and Cohn-Vossen on the size of poles of convex surfaces of revolution. The radius of the smallest ball containing the set of all poles on a Euclidean n-model can be expressed by using the warping function of it.