Geometric structures and differential equations on filtered manifolds

从幂零几何和分析的观点出发，我们一直在发展滤流形上的几何、结构和微分方程的一般理论。最近，作为这些理论的应用，我们对各种混凝土几何结构进行了详细的研究。特别地，将Morimoto的一般理论应用于次黎曼几何，我们得到了如下显著的定理：存在与满足Hormander条件并具有常数一阶逼近的次黎曼流形相联系的典型Cartan联络.我们还确定了直到离散群商为止，其自同构群具有最大维数的齐次次黎曼切触流形.自同构群也分为三个同构类。

From the viewpoint of nilpotent geometry and analysis, we have been developing general theories on geometric, structures and differential equations on filtered manifolds. More recently, as applications of these theories, we have been carrying detailed studies on various concrete geometric structures. In particular, applying the general theory of Morimoto to subriemannian geometry, we have obtained the following remarkable theorem : There exists a canonical Cartan connection associated with a subriemannian manifold satisfying Hormander condition and having constant first order approximation.We have also determined, up to quotient by discrete groups, the homogeneous subriemannian contact manifolds whose automorphism groups are of maximal dimension. The automorphism groups are also classified into three isomorphic classes.