Envelope of mid-hyperplanes of a hypersurface (Q1685531)

Given a pair of points in a smooth convex planar curve, its mid-line is the line that passes through its mid-point and the intersection of the corresponding tangent lines. The envelope of mid-lines of planar curves can be divided into three parts: the affine envelope symmetry set, corresponding to pairs with non-parallel tangent lines; the mid-points parallel tangent locus, corresponding to pairs with parallel tangent lines; the affine evolute, corresponding to coincident points. In this paper, the authors extend the envelope of mid-lines of planar curves to the hypersurfaces.