## Journal of the Mathematical Society of Japan

### Extendible and stably extendible vector bundles over real projective spaces

#### 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 $\zeta$ over the real projective $n$-space $RP^{n}$ is extendible (or stably extendible) to $RP^{m}$ for every $m>n$ in the case where $\zeta$ is the complexification of the tangent bundle of $RP^{n}$ and in the case where $\zeta$ is the normal bundle associated to an immersion of $RP^{n}$ in the Euclidean $(n+k)$-space $R^{n+k}$ or its complexification, and give examples of the normal bundle which is extendible to $RP^{N}$ but is not stably extendible to $RP^{N+1}$.

#### 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

#### 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