Framed hyperstrip affine space distribution

Abstract

A rigged hyperstrip distribution is a special class of hyperstrips. The study of hyperstrips and their generalizations in spaces with various fun­damental groups is of great interest due to numerous applications in mathematics and physics. A special place is occupied by regular hyper­strips, for which the characteristic planes of families of principal tangent hyperplanes do not contain directions tangent to the base surface of the hyperstrip. In this work, we use E. Cartan’s method of external differen­tial forms and the group-theoretic method of G. F. Laptev. In affine space, a hyperstrip distribution is considered, which at each point of the base surface is equipped with a tangent plane and a conjugate tangent line. The specification of the studied hyperstrip distribution in an affine space with respect to a 1st order reference and an existence theorem are given. The fields of affine normals of the 1st kind for Blaschke and Transon are constructed and the conditions for their coincidence are found. The definition of normal affine connection and normal centroaffine connection on the studied framed hyperstrip distribution is given.

Keywords

• hyperstrip
• regular hyperstrip
• hyperstrip distribution
• af­fine normals
• normal affine connection