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arXiv · 0810.0173

Maximal totally complex submanifolds of $\mathbb{H}\mathbb{P}^n$: homogeneity and normal holonomy

Lucio Bedulli·Anna Gori·Fabio Podestà
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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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Lucio Bedulli, Anna Gori, Fabio Podestà. 2008-10-01. Maximal totally complex submanifolds of $\mathbb{H}\mathbb{P}^n$: homogeneity and normal holonomy. https://doi.org/10.1112/blms%2Fbdp081

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