一种用于凸曲面的莫尔斯电码
Un Lemme de Morse pour les surfaces convexes
摘要：
我们描述的“双曲”性质的黎曼曲面层M正则相关的每一个紧凑的三个流形的曲率小于1。更精确地说，如果测地流是一个附在常微分方程上的相空间，那么我们的空间M就是一个附在某个椭圆型方程上的“相空间“，它在几何上描述了具有常数高斯-克罗内克曲率k（k-曲面）的曲面，0<k<1。这些双曲性质是：一般的叶子是稠密的，紧凑的叶子的工会是稠密的，稳定的。他们遵循类似的莫尔斯引理测地线，我们称之为莫尔斯引理凸曲面，并发挥作用的阴影引理。我们还证明了定理的存在性和唯一性的k-曲面。
英文摘要：
We describe the "hyperbolic" properties of a riemann surface lamination M canonically associated to every compact three manifolds of curvature less than 1. More precisely, if the geodesic flow is the phase space attached to an ordinary differential equation, our space M is the "phase space" attached to a certain elliptic equation, which geometrically describes surfaces of constant Gauss-Kronecker curvature k (k-surfaces), 0<k<1. These hyperbolic properties are : a generic leaf is dense, the union of compact leaves is dense, and stability. They follow from an analogous of the Morse lemma for geodesics, which we call Morse lemma for convex surfaces, and which play the role of a shadowing lemma. We also prove theorems on existence and unicity of k-surfaces.
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