Global rigidity for totally nonsymplectic Anosov Zk actions

被引：19

作者：

Kalinin, Boris ^{[1
]}

Sadovskaya, Victoria ^{[1
]}

机构：

[1] Univ S Alabama, Dept Math & Stat, Mobile, AL 36688 USA

来源：

GEOMETRY & TOPOLOGY | 2006年 / 10卷

基金：

美国国家科学基金会;

关键词：

D O I：

10.2140/gt.2006.10.929

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a totally nonsymplectic (TNS) Anosov action of Z(k) which is either uniformly quasiconformal or pinched on each coarse Lyapunov distribution. We show that such an action on a torus is C-infinity-conjugate to an action by affine automorphisms. We also obtain similar global rigidity results for actions on an arbitrary compact manifold assuming that the coarse Lyapunov foliations are topologically jointly integrable.

引用

页码：929 / 954

页数：26

共 21 条

[1] AFFINE ANOSOV DIFFEOMORPHISMS WITH STABLE AND UNSTABLE DIFFERENTIABLE FOLIATIONS [J].

BENOIST, Y ;

LABOURIE, F .

INVENTIONES MATHEMATICAE, 1993, 111 (02) :285-308

[2]

EINSIEDLER M, IN PRESS ISRAEL J MA

[3] The invariant connection of a 1/2-pinched Anosov diffeomorphism and rigidity [J].

Feres, R .

PACIFIC JOURNAL OF MATHEMATICS, 1995, 171 (01) :139-155

[4]

Feres R., 2004, MODERN DYNAMICAL SYS, P103

[5] ANOSOV DIFFEOMORPHISMS ON TORI [J].

FRANKS, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 145 :117-&

[6] Smooth classification of Cartan actions of higher rank semisimple Lie groups and their lattices [J].

Goetze, ER ;

Spatzier, RJ .

ANNALS OF MATHEMATICS, 1999, 150 (03) :743-773

[7] RIGIDITY FOR ANOSOV ACTIONS OF HIGHER RANK LATTICES [J].

HURDER, S .

ANNALS OF MATHEMATICS, 1992, 135 (02) :361-410

[8]

Journe J-L., 1988, Revista Matematica Iberoamericana, V4, P187

[9]

KALININ B, IN PRESS GEOM FUNCT

[10]

Kalinin B., 2001, SMOOTH ERGODIC THEOR, P593, DOI [10.1090/pspum/069/1858547, DOI 10.1090/PSPUM/069/1858547]

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