Hokkaido Mathematical Journal

AGAOKA Yoshio, KANEDA Eiji,

Rigidity of the canonical isometric imbedding of the quaternion projective plane $P^2(\pmb{H})$.

Hokkaido Mathematical Journal, 35 (2006) pp.119-138

Fulltext

PDF

Abstract

In this paper, we investigate isometric immersions of $P^2(\pmb{H})$ into $\pmb{R}^{14}$ and prove that the canonical isometric imbedding $\pmb{f}_0$ of $P^2(\pmb{H})$ into $\pmb{R}^{14}$, which is defined in Kobayashi [11] is rigid in the following strongest sense:Any isometric immersion $\pmb{f}_1$ of a connected open set $U (\subset P^2(\pmb{H}))$ into $\pmb{R}^{14}$ coincides with $\pmb{f}_0$ up to a euclidean transformation of $\pmb{R}^{14}$, i.e., there is a euclidean transformation $a$ of $\pmb{R}^{14}$ satisfying $\pmb{f}_1=a\pmb{f}_0$ on $U$.

MSC(Primary)53C24
MSC(Secondary)53C35, 53B25, 17B20
Uncontrolled KeywordsCurvature invariant, isometric immersion, quaternion projective plane, rigidity,root space decomposition