Lattices and Periodic Geodesics in Pseudoriemannian 2-step Nilpotent Lie Groups

Details Lattices and Periodic Geodesics in Pseudoriemannian 2-step Nilpotent Lie Groups Lattices and Periodic Geodesics in Pseudoriemannian 2-step Nilpotent Lie Groups

2008-02-26

arxiv.org/abs/0802.3771v1

Int. J. Geom. Methods Mod. Phys. 5 (2008) 79-99

Mathematics

Differential Geometry

tp + 23 pp

Scientific paper

10.1142/S0219887808002667

We give a basic treatment of lattices $\Gamma$ in these groups. Certain tori $T_F$ and $T_B$ provide the model fiber and the base for a submersion of $\Gamma\backslash N$. This submersion may not be pseudoriemannian in the usual sense, because the tori may be degenerate. We then begin the study of periodic geodesics in these compact nilmanifolds, obtaining a complete calculation of the period spectrum of certain flat spaces.

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