arXiv subjects

Karin Melnick

Publications and source records attributed to Karin Melnick.

21 records · Page 2Linked to original sources

arXiv2007

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.

math.DS↗

arXiv2006

Compact Lorentz manifolds with local symmetry

We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical, real-analytic, complete Lorentz manifold such that the isometry group of the universal cover has semisimple identity component, then the local isometry orbits in M are roughly fibers of a fiber bundle. A corollary is that if M has a dense local isometry orbit then M is locally homogeneous. The main result is analogous to a theorem of Farb and Weinberger on compact aspherical Riemannian manifolds, and an exposition of their arguments on rational cohomological dimension is included. Some aspects of dynamics on Lorentz manifolds are also presented, including totally geodesic, lightlike, codimension-one foliations associated to unbounded sequences of isometries.

math.DG↗

arXiv2005

Isometric actions of Heisenberg groups on compact Lorentz manifolds

We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions--those for which the dimension of the Heisenberg group is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the assumption they are real-analytic.

math.DG↗