HOW THE DISTANCE BETWEEN SUBSPACES IN THE METRIC OF A SPHERICAL OPENING AFFECTS THE GEOMETRIC STRUCTURE OF A SYMMETRIC SPACE

Abstract

A relationship is found between the metric of a spherical opening on the space of all subspaces of a symmetric space and some numerical characteristic of the subspace. It is known that, for example, in L1 this characteristic takes only two values (i.e. this is a binary space), while in L2 there are infinitely many values. Using the connection found, the necessary conditions for the binarity of a symmetric space were generalized.