This article examines the relationship between geometric Poisson brackets and integrable systems in flat Galilean, and Lorentz manifolds. First, moving frames are used to calculate differential invariants of curves and to write invariant evolution equations. The moving frames are created to ensure that the Galilean moving frame is the limit of the Lorentz one as c → ∞. Then, associated integrab...

In this paper, we find an upper bound of the squared norm of the second fundamental tensor of a complete space-like hypersurface in a Lorentz space form M 1 (c) satisfying some curvature conditions . Then it gives naturally an extension of some theorems of Cheng and Nakagawa ([3]), Ishihara ([7]), Li ([8]) and Nishikawa ([9]). Mathematics Subject Classification: 53C50, 53C25, 53C42.

Mess deduces this result as part of a general theory of domains of dependence in constant curvature Lorentzian 3-manifolds. We give an alternate proof, using an invariant introduced by Margulis [18, 19] and Teichmüller theory. We thank Scott Wolpert for helpful conversations concerning Teichmüller theory. We also wish to thank Paul Igodt and the Algebra Research Group at the Katholieke Universi...

We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (resp., lightlike) manifold.

We construct center-stable and center-unstable manifolds, as well as stable and unstable manifolds, for the nonlinear Klein–Gordon equation with a focusing energy subcritical nonlinearity, associated with a family of solitary waves which is generated from any radial stationary solution by the action of all Lorentz transforms and spatial translations. The construction is based on the graph trans...