%0 Journal Article %T A Few Splitting Criteria for Vector Bundles %A Francesco Malaspina %J Mathematics %D 2008 %I arXiv %X We prove a few splitting criteria for vector bundles on a quadric hypersurface and Grassmannians. We give also some cohomological splitting conditions for rank 2 bundles on multiprojective spaces. The tools are monads and a Beilinson's type spectral sequence generalized by Costa and Mir\'o-Roig. %U http://arxiv.org/abs/0802.1062v1