Stable extendibility of vector bundles over real projective spaces |
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Authors: | Yutaka Hemmi Teiichi Kobayashi |
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Institution: | 1. Department of Mathematics, Faculty of Science, Kochi University, Kochi 780–8520, Japan;2. Asakura-ki 292–21, Kochi 780–8066, Japan |
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Abstract: | Let F be either the real number field R or the complex number field C and RPn the real projective space of dimension n. Theorems A and C in Hemmi and Kobayashi (2008) 2] give necessary and sufficient conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m?n. In this paper, we simplify the theorems and apply them to the tangent bundle of RPn, its complexification, the normal bundle associated to an immersion of RPn in Rn+r(r>0), and its complexification. Our result for the normal bundle is a generalization of Theorem A in Kobayashi et al. (2000) 8] and that for its complexification is a generalization of Theorem 1 in Kobayashi and Yoshida (2003) 5]. |
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Keywords: | primary 55R50 secondary 55N15 |
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