Suppose that $\mathrm{\Sigma }$ is a closed and oriented surface equipped with a Riemannian metric. In the literature, there are three seemingly distinct constructions of open books on the unit (co)tangent bundle of $\mathrm{\Sigma }$, having complex, contact and dynamical flavors, respectively. Each one of these constructions is based on either an admissible divide or an ordered Morse function on $\mathrm{\Sigma }$. We show that the resulting open books are pairwise isotopic provided that the ordered Morse function is adapted to the admissible divide on $\mathrm{\Sigma }$. Moreover, we observe that if $\mathrm{\Sigma }$ has positive genus, then none of these open books are planar and furthermore, we determine the only cases when they have genus one pages.

假设$\mathrm{\Sigma }$是一个配备黎曼度量的封闭且有向的曲面。在文献中，关于单位（余）切丛的开放书籍存在三种看似不同的结构$\mathrm{\Sigma }$，分别具有复杂、接触和动态风味。这些构造中的每一种都基于可接受的除法或有序莫尔斯函数$\mathrm{\Sigma }$。我们表明，只要有序莫尔斯函数适应可接受的划分，所得的开放书是成对同位素的 $\mathrm{\Sigma }$。此外，我们观察到如果$\mathrm{\Sigma }$具有正的亏格，那么这些打开的书都不是平面的，此外，我们确定它们具有一页亏格的唯一情况。