Hokkaido Mathematical Journal

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

Yoshio AGAOKA and Eiji KANEDA

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1285766428

Digital Object Identifier
doi:10.14492/hokmj/1285766428

Mathematical Reviews number (MathSciNet)
MR2289359

Zentralblatt MATH identifier
1121.53035

Subjects
Primary: 53C35: Symmetric spaces [See also 32M15, 57T15]
Secondary: 53B25: Local submanifolds [See also 53C40] 17B20: Simple, semisimple, reductive (super)algebras

Keywords
curvature invariant isometric imbedding complex projective space quaternion projective space root space decomposition

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


Export citation