Normally contracting Lie group actions
Normally contracting Lie group actions
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通常收缩李群作用
DOI：
10.1016/j.topol.2011.12.012
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Yoshihiko
中科院分区：
文献类型：
--
作者：
Inaba;Takashi; Matsumoto;Shigenori; Mitsumatsu;Yoshihiko
令：M× G→ M是n维连通李群G在n+ s+ u维闭C∞流形M上的局部自由右C∞作用，其轨道叶化为F。赋予M一个黎曼度量。对于线性映射A：V→ W的赋范线性空间，记A为A的算子范数，记m（A）为A的同余，即m（A）= inf {Av ∈ V，v= 1}，记TF为F的切丛.根据[2]，作用M称为Anosov作用，如果存在称为Anosov元的元素g∈ G，以及M的切丛TM的连续子丛Es和Eu，使得
Let ϕ: M× G→ M be a locally free right C∞ action of a connected Lie group G of dimension n on a closed C∞ manifold M of dimension n+ s+ u, with orbit foliation F. Endow M with a Riemannian metric. For a linear map A: V→ W of normed linear spaces, we denote by A the operator norm of A, and by m (A) the conorm of A, ie m (A)= inf {Av∣∣ v∈ V, v= 1}.Denote by T F the tangent bundle of F. According to [2], the action ϕ is called an Anosov action if there is an element g∈ G, called an Anosov element, and continuous subbundles Es and Eu of the tangent bundle TM of M such that