1999/05/29 by Luis A. Cordero, Cordero, Luis A., Phillip E. Parker +1
Mathematics · #53B30 #53C30 (Secondary) #53C50 (Primary) 22E25 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:22E25 #msc:53B30 #msc:53C30 #msc:53C50
paper · pdf · doi:10.48550/arxiv.math/9905188
63 pages, requires AMSLaTeX 1.1, dgspp.sty, dgstpp.sty, pproof.sty, remexpp.sty, and rsfspp.sty
arxiv created 1999/05/29 · arxiv updated 2009/11/30
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.