关于叶共形同态
On leafwise conformal diffeomorphisms
摘要：
对于三维黎曼流形$M$和$N$之间的每个同构$φ:M\to N$，一般局部存在两个二维分布$D_{\pm}$，使得$φ$在这两个分布上共形.我们陈述了一个分布是$D_{\pm}$之一充要条件。这些是用自伴和正定算子$(φ_{\ast})^*φ_{\ast}$表示的代数条件。研究了$D_+$和$D_-$的可积性条件。我们还表明，它是可能的，以选择坐标系中，叶共形的复同态是全纯的叶子。
英文摘要：
For every diffeomorphism $φ:M\to N$ between 3--dimensional Riemannian manifolds $M$ and $N$ there are in general locally two 2--dimensional distributions $D_{\pm}$ such that $φ$ is conformal on both of them. We state necessary and sufficient conditions for a distribution to be one of $D_{\pm}$. These are algebraic conditions expressed in terms of the self-adjoint and positive definite operator $(φ_{\ast})^*φ_{\ast}$. We investigate integrability condition of $D_+$ and $D_-$. We also show that it is possible to choose coordinate systems in which leafwise conformal diffeomorphism is holomorphic on leaves.
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