Нормированные плоскости в G-пространствах Буземана неположительной кривизны конического типа

TL;DRAbstract

The geometry of the cone type Busemann G-space, that is nonpositively curved G-space X isometric to its space tangent cone KpX, is studied in the paper. Geodesic spaces of this class have a number of significant geometrical properties. The most significant fact is that the group H of positive homotheties hk with the center p acts on X. Andreev P.D. used the cone type G-spaces earlier for proving the Busemann conjecture about the topological manifold of nonpositively curved G-spaces. The basic result of the paper is the theorem stating that any two rays in X beginning at p are contained in some normed plane. In this case the convex subset isometric to the affine plane equipped with strongly convex norm is considered as the normed plane in the geodesic space X. The proof of the theorem is based on the fact that the convex hull of two non-adjugate rays with common beginning in the vertex p is an angle generated by the integration of the fixed segment images with the ends at these rays und

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