# Extendibility and stable extendibility of vector bundles over lens spaces mod 3

## Abstract

In this paper, we prove that the tangent bundle $\tau(L^{n}(3))$ of the $(2n+1)$-dimensional mod 3 standard lens space $L^{n}(3)$ is stably extendible to $L^{m}(3)$ for every $m \geq n$ if and only if $0 \leq n \leq 3$. Combining this fact with the results obtained in [6],we see that $\tau(L^{2}(3))$ is stably extendible to $L^{3}(3)$, but is not extendible to $L^{3}(3)$. Furthermore, we prove that the $t$-fold power of $\tau(L^{n}(3))$ and its complexification are extendible to $L^{m}(3)$ for every $m \geq n$ if $t \geq 2$, and have a necessary and sufficient condition that the square $\nu^{2}$ of the normal bundle $\nu$ associated to an immersion of $L^{n}(3)$ in the Euclidean $(4n+3)$-space is extendible to $L^{m}(3)$ for every $m \geq n$.

## Journal

• Hiroshima mathematical journal

Hiroshima mathematical journal 35(3), 403-412, 2005-11

Hiroshima University

## Codes

• NII Article ID (NAID)
110004455825
• NII NACSIS-CAT ID (NCID)
AA00664323
• Text Lang
ENG
• ISSN
00182079
• Data Source
NII-ELS

Page Top