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
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
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