ON NIL GEOMETRY

Abstract

Nil geometry is a homogeneous 3-space derived from the Heisenberg matrix group in formula (1), where the matrix multiplication provides the non-commutative addition of translations. The Lie theory, combined with projective geometry [1], makes possible to illustrate some phenomena, e. g. the discrete lattices and the geodesics in Nil. I think the method, aided by computer, gives new possibilities in this field [3] in the future.