Journal of the Mathematical Society of Japan

Extendible and stably extendible vector bundles over real projective spaces

Teiichi KOBAYASHI and Toshio YOSHIDA

Full-text: Open access

Abstract

The purpose of this paper is to study extendibility and stable extendibility of vector bundles over real projective spaces. We determine a necessary and sufficient condition that a vector bundle ζ over the real projective n-space RPn is extendible (or stably extendible) to RPm for every m>n in the case where ζ is the complexification of the tangent bundle of RPn and in the case where ζ is the normal bundle associated to an immersion of RPn in the Euclidean (n+k)-space Rn+k or its complexification, and give examples of the normal bundle which is extendible to RPN but is not stably extendible to RPN+1.

Article information

Source
J. Math. Soc. Japan, Volume 55, Number 4 (2003), 1053-1059.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418763

Digital Object Identifier
doi:10.2969/jmsj/1191418763

Mathematical Reviews number (MathSciNet)
MR2003759

Zentralblatt MATH identifier
1041.55012

Subjects
Primary: 55R50: Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}
Secondary: 57R25: Vector fields, frame fields

Keywords
Vector bundle extendible stably extendible tangent bundle span immersion normal bundle K-theory KO-theory real projective space

Citation

KOBAYASHI, Teiichi; YOSHIDA, Toshio. Extendible and stably extendible vector bundles over real projective spaces. J. Math. Soc. Japan 55 (2003), no. 4, 1053--1059. doi:10.2969/jmsj/1191418763. https://projecteuclid.org/euclid.jmsj/1191418763


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