Open Access
Translator Disclaimer
February 2007 Rigidity of the canonical isometric imbedding of the symplectic group $Sp(n)$
Yoshio AGAOKA, Eiji KANEDA
Hokkaido Math. J. 36(1): 79-110 (February 2007). DOI: 10.14492/hokmj/1285766664

Abstract

In this paper, we discuss the rigidity of $Sp(n)$ as a Riemannian submanifold of $M(n,n;\mathbb{H})$. We prove that the inclusion map $\pmb{f}_0$, which is called the canonical isometric imbedding of $Sp(n)$, is rigid in the following strongest sense: Any isometric immersion $\pmb{f}_1$ of a connected open set $U (\subset Sp(n))$ into $\pmb{R}^{4n^2}\,(\cong M(n,n;\mathbb{H}))$ coincides with $\pmb{f}_0$ up to a euclidean transformation of $\pmb{R}^{4n^2}$, i.e., there is a euclidean transformation $a$ of $\pmb{R}^{4n^2}$ satisfying $\pmb{f}_1=a\pmb{f}_0$ on $U$.

Citation

Download Citation

Yoshio AGAOKA. Eiji KANEDA. "Rigidity of the canonical isometric imbedding of the symplectic group $Sp(n)$." Hokkaido Math. J. 36 (1) 79 - 110, February 2007. https://doi.org/10.14492/hokmj/1285766664

Information

Published: February 2007
First available in Project Euclid: 29 September 2010

zbMATH: 1151.53045
MathSciNet: MR2309823
Digital Object Identifier: 10.14492/hokmj/1285766664

Subjects:
Primary: 53C35
Secondary: 17B20 , 20G20 , 53B25

Keywords: curvature invariant , isometric imbedding , rigidity , symplectic group

Rights: Copyright © 2007 Hokkaido University, Department of Mathematics

JOURNAL ARTICLE
32 PAGES


SHARE
Vol.36 • No. 1 • February 2007
Back to Top