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February 2006 Rigidity of the canonical isometric imbedding of the quaternion projective plane $P^2(\pmb{H})$
Yoshio AGAOKA, Eiji KANEDA
Hokkaido Math. J. 35(1): 119-138 (February 2006). DOI: 10.14492/hokmj/1285766301

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 $U$.

Citation

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Yoshio AGAOKA. Eiji KANEDA. "Rigidity of the canonical isometric imbedding of the quaternion projective plane $P^2(\pmb{H})$." Hokkaido Math. J. 35 (1) 119 - 138, February 2006. https://doi.org/10.14492/hokmj/1285766301

Information

Published: February 2006
First available in Project Euclid: 29 September 2010

zbMATH: 1102.53042
MathSciNet: MR2225085
Digital Object Identifier: 10.14492/hokmj/1285766301

Subjects:
Primary: 53C24
Secondary: 17B20 , 53B25 , 53C35

Keywords: curvature invariant , isometric immersion , quaternion projective plane , rigidity,root space decomposition

Rights: Copyright © 2006 Hokkaido University, Department of Mathematics

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Vol.35 • No. 1 • February 2006
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