We prove that a maximal totally complex submanifold $N^{2n}$ of the quaternionic projective space $\mathbb{H}\mathbb{P}^n$ ($n\geq 2$) is a parallel submanifold, provided one of the following conditions is satisfied: (1) $N$ is the orbit of a compact Lie group of isometries, (2) the restricted normal holonomy is a proper subgroup of ${\rm U}(n)$.
Maximal totally complex submanifolds of $\mathbb{H}\mathbb{P}^n$: homogeneity and normal holonomy / L. Bedulli, A. Gori, F. Podestà. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 41:6(2009), pp. 1029-1040.
Maximal totally complex submanifolds of $\mathbb{H}\mathbb{P}^n$: homogeneity and normal holonomy
A. GoriSecondo
;
2009
Abstract
We prove that a maximal totally complex submanifold $N^{2n}$ of the quaternionic projective space $\mathbb{H}\mathbb{P}^n$ ($n\geq 2$) is a parallel submanifold, provided one of the following conditions is satisfied: (1) $N$ is the orbit of a compact Lie group of isometries, (2) the restricted normal holonomy is a proper subgroup of ${\rm U}(n)$.
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