论文标题
地球凸度和封闭的nilpotent相似性歧管
Geodesic convexity and closed nilpotent similarity manifolds
论文作者
论文摘要
一些Nilpotent Lie组具有类似于作用于欧几里得空间的相似性群体的转化组。我们称这样的对为nilpotent相似性结构。所有Carnot群体及其扩张是如此。我们概括了一个炸的定理：具有nilpotent相似性结构的闭合歧管是完整的或辐射的，在后一种情况下，对于被剥夺点的空间的结构而言是完整的。证明依赖于在一个环境中的凸率参数的概括，在这种情况下，在Lie代数给出的坐标中，我们研究了测地段，而不是线性段。我们展示了对封闭歧管的经典后果，其几何形状在等级一个对称空间的边界上建立。
Some nilpotent Lie groups possess a transformation group analogous to the similarity group acting on the Euclidean space. We call such a pair a nilpotent similarity structure. It is notably the case for all Carnot groups and their dilatations. We generalize a theorem of Fried: closed manifolds with a nilpotent similarity structure are either complete or radiant and, in the latter case, complete for the structure of the space deprived of a point. The proof relies on a generalization of convexity arguments in a setting where, in the coordinates given by the Lie algebra, we study geodesic segments instead of linear segments. We show classic consequences for closed manifolds with a geometry modeled on the boundary of a rank one symmetric space.
