Hokkaido Mathematical Journal

AGAOKA Yoshio, KANEDA Eiji,

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

Hokkaido Mathematical Journal, 35 (2006) pp.753-766

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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].

MSC(Primary)53C35
MSC(Secondary)53B25, 17B20
Uncontrolled Keywordscurvature invariant, isometric imbedding, complex projective space, quaternion projective space, root space decomposition