Splitting 3-plane sub-bundles over the product of two real projective spaces
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 la...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Sociedade Brasileira de Matemática
2003-11-01
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Series: | Boletim da Sociedade Paranaense de Matemática |
Subjects: | |
Online Access: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7506/4324 |
Summary: | 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. |
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ISSN: | 0037-8712 2175-1188 |