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. Gori
Secondo
;
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 ${\rm U}(n)$.
Totally complex submanifolds
Settore MAT/03 - Geometria
2009
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/162245
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