6 research outputs found
On Lorentz dynamics : From group actions to warped products via homogeneous spaces
We show a geometric rigidity of isometric actions of non compact (semisimple)
Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped
product structure of a Lorentz manifold with constant curvature by a Riemannian
manifold
Actions of noncompact semisimple groups on Lorentz manifolds
The above title is the same, but with "semisimple" instead of "simple," as
that of a notice by N. Kowalsky. There, she announced many theorems on the
subject of actions of simple Lie groups preserving a Lorentz structure.
Unfortunately, she published proofs for essentially only half of the announced
results before her premature death. Here, using a different, geometric
approach, we generalize her results to the semisimple case, and give proofs of
all her announced results.Comment: 25 pp, to appear in Geometric and Functional Analysis sharpened thm
1.9 to give global description of actions in all cases; added section 8 on
structure of orbits of Riemannian type and how Riemannian and Lorentzian
orbits meet around degenerate set; many minor corrections and improvements
thanks to referee's comment
Pseudo-Conformal Actions of the M{\"o}bius Group
We study compact connected pseudo-Riemannian manifolds on which the
conformal group acts essentially and transitively.
We prove, in particular, that if the non-compact semi-simple part of
is the M{\"o}bius group, then is conformally
flat
Pseudo-Conformal Actions of the M{\"o}bius Group
We study compact connected pseudo-Riemannian manifolds on which the conformal group acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of is the M{\"o}bius group, then is conformally flat
PSEUDO-CONFORMAL ACTIONS OF THE MÖBIUS GROUP
We study compact connected pseudo-Riemannian manifolds on which the conformal group acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of is the Möbius group, then is conformally flat