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 $U$.
Publié le : 2006-02-15
Classification:
Curvature invariant,
isometric immersion,
quaternion projective plane,
rigidity,root space decomposition,
53C24,
53C35,
53B25,
17B20
@article{1285766301,
author = {AGAOKA, Yoshio and KANEDA, Eiji},
title = {Rigidity of the canonical isometric imbedding of the quaternion projective plane $P^2(\pmb{H})$},
journal = {Hokkaido Math. J.},
volume = {35},
number = {1},
year = {2006},
pages = { 119-138},
language = {en},
url = {http://dml.mathdoc.fr/item/1285766301}
}
AGAOKA, Yoshio; KANEDA, Eiji. Rigidity of the canonical isometric imbedding of the quaternion projective plane $P^2(\pmb{H})$. Hokkaido Math. J., Tome 35 (2006) no. 1, pp. 119-138. http://gdmltest.u-ga.fr/item/1285766301/