论文标题
通过切割基因座的纤维分解的地球复杂性
Geodesic complexity via fibered decompositions of cut loci
论文作者
论文摘要
riemannian歧管的地球复杂性是数值等轴测图不变的，它取决于其切割基因座的结构。在本文中，我们研究了切割基因座的分解，其组件以方便的方式切好的切割基因座纤维。我们在此类分解方面建立了一个新的上层界限，以实现地球复杂性。作为一种应用，我们获得了某些类别均匀流形的测地量复杂性的估计。特别是，我们计算复杂和四基因开枪空间的测量复杂性及其标准的对称度量标准。
The geodesic complexity of a Riemannian manifold is a numerical isometry invariant that is determined by the structure of its cut loci. In this article we study decompositions of cut loci over whose components the tangent cut loci fiber in a convenient way. We establish a new upper bound for geodesic complexity in terms of such decompositions. As an application, we obtain estimates for the geodesic complexity of certain classes of homogeneous manifolds. In particular, we compute the geodesic complexity of complex and quaternionic projective spaces with their standard symmetric metrics.
