A Cohomological criterion for the splitting of vector bundles on ${\mathbb{P}}^{n_1}\times \cdots \times {\mathbb{P}}^{n_s}$

In this paper we study the cohomological criterion for the splitting of vector bundles on multiprojective spaces ${\mathbb{P}}^{n_1}\times \dots \times {\mathbb{P}}^{n_s}$. We also give a generalization of vanishing cohomological criteria for vector bundles on ${\mathbb{P}}^n\times \dots \times {\mathbb{P}}^n$.