论文标题
等量旗歧管的索引
The index of equidimensional flag manifolds
论文作者
论文摘要
在本文中，我们考虑了$ p $正交子空间的标志歧管，该子空间具有相等的尺寸，该子空间携带了订单$ p $的循环群的动作。我们提供了相关的Fadell-Husseini指数的完整计算。对于Grassmann歧管$ g_n（\ MathBb {r}^{2n}）$，这可能被认为是Baralić等人[Forum Math。，30（2018），第1539---1572页的计算的奇数主要版本。这些结果对凸体的$ p $倍正交阴影产生了几何后果。
In this paper, we consider the flag manifold of $p$ orthogonal subspaces of equal dimension which carries an action of the cyclic group of order $p$. We provide a complete calculation of the associated Fadell-Husseini index. This may be thought of as an odd primary version of the computations of Baralić et al [Forum Math., 30 (2018), pp. 1539--1572] for the Grassmann manifold $G_n(\mathbb{R}^{2n})$. These results have geometric consequences for $p$-fold orthogonal shadows of a convex body.
