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.
@article{7506,
title = {Splitting 3-plane sub-bundles over the product of two real projective spaces - doi: 10.5269/bspm.v21i1-2.7506},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v21i1-2.7506},
language = {EN},
url = {http://dml.mathdoc.fr/item/7506}
}
Mello, Maria Hermínia P. L.; da Silva, Mário Olivero Marques. Splitting 3-plane sub-bundles over the product of two real projective spaces - doi: 10.5269/bspm.v21i1-2.7506. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v21i1-2.7506. http://gdmltest.u-ga.fr/item/7506/