## Hokkaido Mathematical Journal

### A lower bound for the class number of $P^n(\pmb{C})$ and $P^n(\pmb{H})$

#### Abstract

We obtain new lower bounds on the codimension of local isometric imbeddings of complex and quaternion projective spaces. We show that any open set of the complex projective space $P^n(\pmb{C})$ (resp. quaternion projective space $P^n(\pmb{H})$) cannot be locally isometrically imbedded into the euclidean space of dimension $4n-3$ (resp. $8n-4$). These estimates improve the previously known results obtained in [2] and [7].

#### Article information

Source
Hokkaido Math. J., Volume 35, Number 4 (2006), 753-766.

Dates
First available in Project Euclid: 29 September 2010

https://projecteuclid.org/euclid.hokmj/1285766428

Digital Object Identifier
doi:10.14492/hokmj/1285766428

Mathematical Reviews number (MathSciNet)
MR2289359

Zentralblatt MATH identifier
1121.53035

#### Citation

AGAOKA, Yoshio; KANEDA, Eiji. A lower bound for the class number of $P^n(\pmb{C})$ and $P^n(\pmb{H})$. Hokkaido Math. J. 35 (2006), no. 4, 753--766. doi:10.14492/hokmj/1285766428. https://projecteuclid.org/euclid.hokmj/1285766428