Download zipped PostScript files of these joint papers with L. A. Cordero:

Geodesic Surfaces in the Heisenberg Group

The following page shows two surfaces comprised of all the "equatorial" geodesics emanating from the identity element in the 3-dimensional Heisenberg group. The first picture is with a Lorentzian metric of signature (- - +), the second is with (+ - -), and the third is with (+ + -). To see "inside" the null cone, the third is rotated relative to the other two.

Geodesic Surfaces

In both pictures, the curves radiating or emanating outward from the origin (0,0,0) are geodesics and the "concentric circles" transverse to them are curves of constant t -value, with geodesic parameter t.

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