Splitting 3-plane sub-bundles over the product of two real projective spaces - doi: 10.5269/bspm.v21i1-2.7506

Résumé

Let \alpha be a real vector bundle of fiber dimension three over the product RP(m)× RP(n) which splits as a Whitney sum of line bundles. We show that the necessary and sufficient conditions for to embed as a sub-bundle of a certain family of vector bundles \alpha of fiber dimension m+n is the vanishing of the last three Stiefel-Whitney classes of the virtual bundle0 \beta − \alpha . Among the target bundles we consider the tangent bundle.