In this paper we discuss the rigidity of the canonical isometric imbedding $\pmb{f}_0$ of the Hermitian symmetric space $Sp(n)/U(n)$ into the Lie algebra $\mathfrak{sp}(n)$.
We will show that if $n \ge 2$, then $\pmb{f}_0$ is strongly rigid, i.e., for any isometric immersion $\pmb{f}_1$
of a connected open set $U$ of $Sp(n)/U(n)$ into $\mathfrak{sp}(n)$ there is a euclidean transformation $a$ of $\mathfrak{sp}(n)$ satisfying $\pmb{f}_1=a\pmb{f}_0$ on $U$.
@article{1277472869,
author = {AGAOKA, Yoshio and KANEDA, Eiji},
title = {Rigidity of the canonical isometric imbedding of the Hermitian symmetric space $Sp(n)/U(n)$},
journal = {Hokkaido Math. J.},
volume = {36},
number = {4},
year = {2007},
pages = { 615-640},
language = {en},
url = {http://dml.mathdoc.fr/item/1277472869}
}
AGAOKA, Yoshio; KANEDA, Eiji. Rigidity of the canonical isometric imbedding of the Hermitian symmetric space $Sp(n)/U(n)$. Hokkaido Math. J., Tome 36 (2007) no. 4, pp. 615-640. http://gdmltest.u-ga.fr/item/1277472869/