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

Abstract

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.

tp + 23 pp

References in corpus (1)

• Skewadjoint operators on pseudoeuclidean spaces

Cited by in corpus (4)

• Curvature structure of self-dual 4-manifolds
• Complete classification of $H$-type algebras: I
• Naturally reductive pseudo Riemannian 2-step nilpotent Lie groups
• Isometric actions on pseudo-Riemannian nilmanifolds