论文标题
$ \ mathrm {sp} _ {\ mathrm {ell}}}^{+}（2n）$的因果特征
A causal characterisation of $\mathrm{Sp}_{\mathrm{ell}}^{+}(2n)$
论文作者
论文摘要
我们表明，线性符号组$ \ mathrm {sp}（2n）$上的自然结合不变锥结构在正上全球夸张的椭圆形区域$ \ mathrm {sp} _ {\ mathrm {\ mathrm {ell}}}}^{+}^{+}（2n）$。这回答了Abbondandolo，Benedetti和Polterovich的一个问题，并显示了这些作者对该地区元素否认的双重不变Lorentzian距离函数的公式。此外，我们在\ mathrm {sp}（2n）$ in Cone结构的因果关系方面给出了积极的椭圆形区域和$ -ID \ in $ -id \ in的表征。
We show that the natural conjugation invariant cone structure on the linear symplectic group $\mathrm{Sp}(2n)$ is globally hyperbolic in the positively elliptic region $\mathrm{Sp}_{\mathrm{ell}}^{+}(2n)$. This answers a question by Abbondandolo, Benedetti and Polterovich and shows a formula for a bi-invariant Lorentzian distance function dened by these authors for elements in this region. Moreover we give a characterisation of the positively elliptic region and of $-id \in\mathrm{Sp}(2n)$ in terms of the causality of this cone structure.
