论文标题
分子型和切线锥体中的切线锥
Tangent groupoid and tangent cones in sub-Riemannian geometry
论文作者
论文摘要
令$ x_1，\ cdots，x_m $为矢量字段，满足Hörmander的Lie支架生成条件，以平滑的歧管$ M $。我们通过构建Space $ M \ times M \ Times M \ Times \ Mathbb {r} _+^\ times $使用子riemannian Metric来概括Connes的切线群。我们利用空间在Gromov-Hausdorff距离的意义上计算次曼尼亚计度量的所有切线。这概括了贝拉奇的结果。
Let $X_1,\cdots,X_m$ be vector fields satisfying Hörmander's Lie bracket generating condition on a smooth manifold $M$. We generalise Connes's tangent groupoid, by constructing a completion of the space $M\times M\times \mathbb{R}_+^\times$ using the sub-Riemannian metric. We use our space to calculate all the tangent cones of the sub-Riemannian metric in the sense of the Gromov-Hausdorff distance. This generalises a result of Bellaïche.
