On manifolds having some restricted ideal boundaries

The theory of the ideal boundary has arisen as a method of a study of noncompact manifolds. In this paper we shall investigate properties of manifolds whose ideal boundaries satisfy some conditions related to the Tits metric. In Section 2 we shall consider in what conditions the Tits topology is equivalent to the sphere topology and in Section 3 the property of points at infinity which characterize the R-factor. Furthermore, in Section 4 we shall give a sufficient condition for a projective map to be isometríc.Partially supported by Grant-in-Aid for Encouragement of Young Scientists (No. 01740011), The Ministry of Education, Science and Culture, Japan.