Exact transverse line fields and projective billiards in a ball (Q1365209)

This paper continues the series by the author in which he studies projective billiards. A projective billiard generalizes the regular one. Instead of the classical ``the angle of incidence is equal to the angle of reflection'', it is now required that the incoming and outgoing rays, the tangent line to the boundary and a special transverse line constitute a harmonic quadruple. The field of special transverse lines plays the role of the normal lines to the boundary in the regular billiards. In the multidimensional case all these lines need, in addition, to lie in one 2-plane. This defines the outgoing ray uniquely. The author generalizes to any dimension his previous results on 2D projective billiards.