Characteristic classes of vector bundles over \(\mathbb R\mathbb P(h)\times \mathbb H\mathbb P(k)\) (Q880147)

The authors give an explicit formula for the total Stiefel-Whitney classes of vector bundles over the spaces \({\mathbb R}{\mathbb P}^h\times {\mathbb H}{\mathbb P}^k\). As a corollary, they prove that there are no non-bounding involutions of \({\mathbb R}{\mathbb P}^h\times {\mathbb H}{\mathbb P}^k\) that fix \({\mathbb R}{\mathbb P}^{2n+1}\times {\mathbb H}{\mathbb P}^k\).