## Hiroshima Mathematical Journal

### Stable extendibility of some complex vector bundles over lens spaces and Schwarzenberger’s theorem

#### Abstract

We obtain conditions for stable extendibility of some complex vector bundles over the $(2n + 1)$-dimensional standard lens space $L^n(p) \operatorname{mod} p$, where $p$ is a prime. Furthermore, we study stable extendibility of the bundle $\pi^*_n (\tau(\mathbf{C}P^n))$ induced by the natural projection $\pi_n : L^n(p)\to \mathbf{C}P^n$ from the complex tangent bundle $\tau(\mathbf{C}P^n)$ of the complex projective $n$-space $\mathbf{C}P^n$. As an application, we have a result on stable extendibility of $\tau(\mathbf{C}P^n)$ which gives another proof of Schwarzenberger’s theorem.

#### Article information

Source
Hiroshima Math. J., Volume 46, Number 3 (2016), 333-341.

Dates
Revised: 30 August 2016
First available in Project Euclid: 25 February 2017

https://projecteuclid.org/euclid.hmj/1487991625

Digital Object Identifier
doi:10.32917/hmj/1487991625

Mathematical Reviews number (MathSciNet)
MR3614301

Zentralblatt MATH identifier
1367.55008

#### Citation

Hemmi, Yutaka; Kobayashi, Teiichi. Stable extendibility of some complex vector bundles over lens spaces and Schwarzenberger’s theorem. Hiroshima Math. J. 46 (2016), no. 3, 333--341. doi:10.32917/hmj/1487991625. https://projecteuclid.org/euclid.hmj/1487991625