On Legendrian Embbeddings into Open Book Decompositions

We study Legendrian embeddings of a compact Legendrian submanifold $L$ sitting in a closed contact manifold $(M,\xi )$ whose contact structure is supported by a (contact) open book $\mathcal{O}\mathcal{B}$ on $M$. We prove that if $\mathcal{O}\mathcal{B}$ has Weinstein pages, then there exist a contact structure ${\xi }^{\mathrm{\prime }}$ on $M$, isotopic to $\xi$ and supported by $\mathcal{O}\mathcal{B}$, and a contactomorphism $f:(M,\xi )\to (M,{\xi }^{\mathrm{\prime }})$ such that the image $f(L)$ of any such submanifold can be Legendrian isotoped so that it becomes disjoint from the closure of a page of $\mathcal{O}\mathcal{B}$.