## Hiroshima Mathematical Journal

### The power of the normal bundle associated to an immersion of $\RP^n$, its complexification and extendibility

#### Abstract

The purpose of this paper is to establish the formulas on the power of the normal bundle associated to an immersion of the real projective space $\RP^n$ in the Euclidean space $\R^{n+k}$, and apply them to the problem of extendibility and stable extendibility. Furthermore, we give an example of a $2$-dimensional $\R$-vector bundle over $\RP^2$ that is stably extendible to $\RP^3$ but is not extendible to $\RP^3$.

#### Article information

Source
Hiroshima Math. J., Volume 37, Number 1 (2007), 101-109.

Dates
First available in Project Euclid: 11 April 2007

https://projecteuclid.org/euclid.hmj/1176324097

Digital Object Identifier
doi:10.32917/hmj/1176324097

Mathematical Reviews number (MathSciNet)
MR2308526

Zentralblatt MATH identifier
1129.57034

#### Citation

Hemmi, Yutaka; Kobayashi, Teiichi; Lwin Oo, Min. The power of the normal bundle associated to an immersion of $\RP^n$, its complexification and extendibility. Hiroshima Math. J. 37 (2007), no. 1, 101--109. doi:10.32917/hmj/1176324097. https://projecteuclid.org/euclid.hmj/1176324097