Abstract
The study of hyperbands and their generalizations in spaces with different fundamental groups is of great interest in connection with numerous applications in mathematics and physics. In this paper, we study a special class of hyperbands, i. e., centrally equipped hyperbands. A hyperband Hm (m ≥ 2) is said to be centrally rigged if the rigging lines in the normals of the 1st kind of the base surface pass through one (the center of the rigging). The article gives a task of a centrally equipped hyperband in the 1st order frame. A sequence of fundamental geometric objects of a hyperstrip with central framing is constructed. An existence theorem for a hyperband with a central framing is proved. It is proved that a hyperstrip with central framing and framing in the sense of Cartan induces a projective connection obtained by projection, where the projection center at each point is the Cartan plane. The spans of the components of the curvature-torsion tensor of the constructed connection are found.
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