ABELIAN ACTIONS WITH GLOBALLY HYPOELLIPTIC LEAFWISE LAPLACIAN AND RIGIDITY

被引：3

作者：

Damjanovic, Danijela ^{[1
]}

机构：

[1] Kungliga Tekniska Hgskolan, Dept Math, Lindstedtsvgen 25, S-10044 Stockholm, Sweden

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2016年 / 129卷

关键词：

VECTOR-FIELDS; LOCAL RIGIDITY; ACTIONS I;

D O I：

10.1007/s11854-016-0018-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：139 / 163

页数：25

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