Splitting 3-plane sub-bundles over the product of two real projective spaces

• Main Authors: Maria Hermínia de Paula Leite Mello, Mário Olivero Marques da Silva
• Format: Article
• Language: English
• Published: Sociedade Brasileira de Matemática 2003-11-01
• Series: Boletim da Sociedade Paranaense de Matemática
• Subjects: Whitney sum of line bundles; vector bundle of fiber dimension three over the product RP(m)×RP(n).
• Online Access: http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7506/4324
• ISSN: 0037-8712; 2175-1188

Let α 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 α to embed as a sub-bundle of a certain family of vector bundles β of fiber dimension m+n is the vanishing of the last three Stiefel-Whitney classes of the virtual bundle0 β−α. Among the target bundles β we consider the tangent bundle.