E_7, Wirtinger inequalities, Cayley 4-form, and homotopy
E_7, Wirtinger inequalities, Cayley 4-form, and homotopy
复制标题
DOI：
10.1215/00127094-2008-061
复制
发表时间：
2006-08
影响因子：
2.5
通讯作者：
V. Bangert;M. Katz;S. Shnider;S. Weinberger
中科院分区：
文献类型：
--
作者：
V. Bangert;M. Katz;S. Shnider;S. Weinberger
本文研究了C. Loewner和M.格罗莫夫，使用一个概括的Wirtinger不等式的comass。利用由BS归纳建立的分类空间BS的模型，证明了某些两点齐次流形的对称度量不是这些流形上的系统最优度量.我们指出了意想不到的作用所发挥的特殊李代数E7在收缩几何，通过计算Wirtinger常数。利用收缩比控制的拉回技术，我们计算了四元数射影平面的最优收缩比，模的存在性的乔伊斯流形与自旋（7）holonomy和单位中维Betti数.
We study optimal curvature-free inequalities of the type discovered by C. Loewner and M. Gromov, using a generalisation of the Wirtinger inequality for the comass. Using a model for the classifying space BS built inductively out of BS, we prove that the symmetric metrics of certain two-point homogeneous manifolds turn out not to be the systolically optimal metrics on those manifolds. We point out the unexpected role played by the exceptional Lie algebra E7 in systolic geometry, via the calculation of Wirtinger constants. Using a technique of pullback with controlled systolic ratio, we calculate the optimal systolic ratio of the quaternionic projective plane, modulo the existence of a Joyce manifold with Spin(7) holonomy and unit middle-dimensional Betti number.