Torsion pairs and recollements of extriangulated categories

In this article, we prove that if $(\mathcal{A},\mathcal{B},\mathcal{C})$ is a recollement of extriangulated categories, then torsion pairs in $\mathcal{A}$ and $\mathcal{C}$ can induce torsion pairs in $\mathcal{B}$, and the converse holds under natural assumptions. Besides, we give mild conditions on a cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding abelian quotients to form a recollement of abelian categories.