论文标题
亚riemannian几何形状的临界点处指数图的局部非注射率
Local non-injectivity of the exponential map at critical points in sub-Riemannian geometry
论文作者
论文摘要
我们证明，在某些临界点的任何社区中，亚riemannian指数图都不是注入性的。也就是说，它的行为不像$ f（x）= x^3 $在其临界点$ x = 0 $的真实图像中的行为。结果，我们根据空间的度量结构来表征理想的亚riemannian歧管中的共轭点。该证明使用了相关变分问题的希尔伯特不变式组成部分。
We prove that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points. Namely that it does not behave like the injective map of reals given by $f(x) = x^3$ near its critical point $x = 0$. As a consequence, we characterise conjugate points in ideal sub-Riemannian manifolds in terms of the metric structure of the space. The proof uses the Hilbert invariant integral of the associated variational problem.
