Nilpotent Lie Groups

Pseudoriemannian Nilpotent Lie Groups, 30 June 2005, rev. 3 October 2005.
This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Françoise, G. L. Naber and Tsou S. T. Oxford: Elsevier, 2006. vol.4, pp.94--104.
Bibliography of pseudoRiemannian nilpotent Lie groups, 27 Jan 2010; updated 31 Mar 2013.
For my own convenience, and I hope for the community as well, I will maintain this with periodic updates (listings appreciated) for at least the next few years.
Download joint papers with L. A. Cordero : Download zipped PostScript files of these joint papers with C. Jang:

Geodesic Surfaces and Conjugate Loci in the Heisenberg Group

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

Geodesic Surfaces and Conjugate Loci

In all 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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