Global deformations of certain rational almost homogeneous projective bundles

We study global deformations of certain projective bundles over projective spaces. We show that any projective global deformation of a projective bundle over ${\text{bP}}^1$ carries the structure of a projective bundle over some projective space. Furthermore, we construct examples in arbitrary dimension $\ge 3$ of almost homogeneous Fano projective bundles over ${\text{bP}}^2$ which can be globally deformed to non-almost homogeneous manifolds.