论文标题
在heintze carnot型中夹紧曲率
Pinched Curvature in Heintze Groups of Carnot-type
论文作者
论文摘要
排名对称空间具有可解决的组模型，该模型对较大的lie基团具有概括为nilpotent组的一维延伸。通过检查这些对称空间的某些度量特性，我们激励并证明了Carnot-type组上的类似左右不变的Riemannian指标的存在。这些指标遵守某些自然曲率捏合特性，在特殊情况下，我们表明这种捏合是最佳的，对Belegradek和Kapovitch的结果有吸引力。
Rank-one symmetric spaces carry a solvable group model which have a generalization to a larger class of Lie groups that are one-dimensional extensions of nilpotent groups. By examining some metric properties of these symmetric spaces, we motivate and prove the existence of analogous left-invariant, Riemannian metrics on Heintze groups of Carnot-type. These metrics adhere to certain natural curvature pinching properties, and we show in a special case that this pinching is optimal, appealing to a result of Belegradek and Kapovitch.
