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Simple problems emphasizing the significance of the ratio of similarity in situations concerning circle, square and their parts.
Simple problems emphasizing the significance of the ratio of similarity in situations concerning circle, square and their parts.
Der Artikel beschäftigt sich mit einigen Eigenschaften von hyperbolischen, d. h. gebrochen-affinen, Transformationen, welche für die Bilder konvexer Polyeder bei solchen Transformationen von Bedeutung sind. Es wird eine explizite Darstellung des Bildes eines konvexen Polyeders durch Ecken und Kanten des Urbildpolyeders gewonnen, die Konvexität des Bildes und das Bild des relativen Inneren einer konvexen Menge untersucht.
It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic -space which, in the projective model for , is just the intersection of with a projective polyhedron whose vertices are all outside and whose edges all meet . We classify hyperideal polyhedra, up to isometries of , in terms of their combinatorial type and of their dihedral angles.
This is a brief review of how sigma models in Projective Superspace have become important tools for constructing new hyperkähler metrics.