论文标题
对称空间的索引猜想
The Index Conjecture for Symmetric Spaces
论文作者
论文摘要
1980年，Onishchik引入了Riemannian对称空间的索引，这是（正确）完全大地测量的Submanifold的最小编成。他计算出级别的对称空间小于或等于2的指数，但是对于更高的排名，尚不清楚如何解决该问题。在较早的论文中，我们开发了几种解决此问题的方法，这使我们能够计算许多对称空间的索引。我们的系统方法导致了如何计算索引的猜想。本文的目的是验证猜想。
In 1980, Onishchik introduced the index of a Riemannian symmetric space as the minimal codimension of a (proper) totally geodesic submanifold. He calculated the index for symmetric spaces of rank less than or equal to 2, but for higher rank it was unclear how to tackle the problem. In earlier papers we developed several approaches to this problem, which allowed us to calculate the index for many symmetric spaces. Our systematic approach led to a conjecture for how to calculate the index. The purpose of this paper is to verify the conjecture.
