How the distance between subspaces in the metric of a spherical opening affects the geometric structure of a symmetric space

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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.

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Stepan I. Strakhov

Samara National Research University

Author for correspondence.
ORCID iD: 0000-0002-2905-9124

assistant of the Department of Functional Analysis and Function Theory

Russian Federation, Samara


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