English

Actions with globally hypoelliptic leafwise Laplacian and rigidity

Dynamical Systems 2013-07-23 v2

Abstract

We prove several results concerning smooth Rk\mathbb R^k actions with the property that their leafwise Laplacian is globally hypoelliptic. Such actions are necessarily uniquely ergodic and minimal, and cohomology is often finite-dimensional, even trivial. Further we consider a class of examples of R2\mathbb R^2 actions on 2-step nilmanifolds, which have globally hypoelliptic leafwise Laplacian, and we show transversal local rigidity under certain Diophantine conditions.

Keywords

Cite

@article{arxiv.1307.3661,
  title  = {Actions with globally hypoelliptic leafwise Laplacian and rigidity},
  author = {Danijela Damjanovic},
  journal= {arXiv preprint arXiv:1307.3661},
  year   = {2013}
}
R2 v1 2026-06-22T00:50:57.393Z