论文标题
在$ \ Mathcal {h}^{\ Mathrm {helprm {help}}（4）$中的平移表面上的简单封闭的大地测量学和分类定理（4）$
Simple closed geodesics on hyperelliptic translation surfaces and classification theorem for translation surfaces in $\mathcal{H}^{\mathrm{hyp}}(4)$
论文作者
论文摘要
在本文中，我们提供了最大数量$ n $的数字，以便我们可以采用$ n $简单的封闭的大地测量学，而无需奇点，而无奇异性则是彼此之间的不相交的，以在超elliptipic组件$ \ MATHCAL {h}^h}^{\ rm {hyp rm {herp}}}}（2g-2）（2g-2）（2g-2）$和$ \ nathcalcal { G-1）$。最大值与双曲线表面的情况不同。我们还为$ \ Mathcal {h}^{\ Mathrm {herp}}}（4）$在其欧几里得结构中提供了一个分类定理。
In this paper, we give the maximum of the numbers $n$ such that we can take $n$ simple closed geodesics without singularities that are disjoint to each other for translation surfaces in the hyperelliptic components $\mathcal{H}^{\rm {hyp}}(2g-2)$ and $\mathcal{H}^{\rm{hyp}}(g-1, g-1)$. The maximum is different from that of the case of hyperbolic surfaces. We also give a classification theorem for translation surfaces in $\mathcal{H}^{\mathrm{hyp}}(4)$ with respect to their Euclidean structures.
