## Journal of the Mathematical Society of Japan

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

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

Teiichi KOBAYASHI and Toshio YOSHIDA

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

#### 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

**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