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

#### 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 ${\rm U}(n)$.
##### Scheda breve Scheda completa Scheda completa (DC)
Totally complex submanifolds
Settore MAT/03 - Geometria
2009
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
##### Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/162245
• ND
• 3
• 2