Pseudoriemannian 2-Step Nilpotent Lie Groups

Details Pseudoriemannian 2-Step Nilpotent Lie Groups Pseudoriemannian 2-Step Nilpotent Lie Groups

1999-05-29

arxiv.org/abs/math/9905188v1

Mathematics

Differential Geometry

63 pages, requires AMSLaTeX 1.1, dgspp.sty, dgstpp.sty, pproof.sty, remexpp.sty, and rsfspp.sty

Scientific paper

We begin a systematic study of these spaces, initially following along the lines of Eberlein's comprehensive study of the Riemannian case. In particular, we integrate the geodesic equation, discuss the structure of the isometry group, and make a study of lattices and periodic geodesics. Some major differences from the Riemannian theory appear. There are many flat groups (versus none), including Heisenberg groups. While still a semidirect product, the isometry group can be strictly larger than the obvious analogue. Everything is illustrated with explicit examples. We introduce the notion of pH-type, which refines Kaplan's H-type and completes Ciatti's partial extension. We give a general construction for algebras of pH-type.

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