CR Embedded Submanifolds of CR Manifolds
CR Embedded Submanifolds of CR
Manifolds
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CR 歧管的 CR 嵌入式子歧管
DOI：
10.1090/memo/1241
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
A. Gover
中科院分区：
文献类型：
--
作者：
Sean N. Curry;A. Gover
我们以一种类似于黎曼子流形理论中的里奇演算的方式，为CR流形的CR嵌入子流形发展了一套完整的局部理论。特别地，我们确立了子流形与周围标准拖拉丛之间的微妙关系，这使我们能够通过一个CR高斯公式将各自的法向嘉当（或拖拉）联络联系起来。CR嵌入的CR不变拖拉演算根据任意（适当适配的）周围接触形式的田中和韦伯斯特演算具体地展开。这使得能够直接且明确地计算嵌入的伪厄米特不变量，这些不变量也是CR不变的。用更朴素的方法来找到和计算这些不变量是极其困难的。最后，我们建立了黎曼子流形理论中经典博内定理的一个CR类似物。
We develop a complete local theory for CR embedded submanifolds of CR manifolds in a way which parallels the Ricci calculus for Riemannian submanifold theory. In particular, we establish the subtle relationship between the submanifold and ambient standard tractor bundles, allowing us to relate the respective normal Cartan (or tractor) connections via a CR Gauss formula. The CR invariant tractor calculus of CR embeddings is developed concretely in terms of the Tanaka-Webster calculus of an arbitrary (suitably adapted) ambient contact form. This enables straightforward and explicit calculation of the pseudohermitian invariants of the embedding which are also CR invariant. These are extremely difficult to find and compute by more na\"ive methods. We conclude by establishing a CR analogue of the classical Bonnet theorem in Riemannian submanifold theory.