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Bulletin of the London Mathematical Society Advance Access published online on September 21, 2009
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdp081
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© 2009 London Mathematical Society

Maximal totally complex submanifolds of HPn: homogeneity and normal holonomy

Lucio Bedulli

Dipartimento di Matematica Sapienza
Università di Roma
P.le Aldo Moro 2
00185 Roma
Italy

Anna Gori

Dipartimento di Matematica
Università di Bologna
Piazza di Porta S. Donato 5
40126 Bologna
Italy
gori@math.unifi.it

Fabio Podestá

Dipartimento di Matematica e Applicazioni Per l'Architettura
Università di Firenze
Piazza Ghiberti 27, 50122 Firenze
Italy
podesta@math.unifi.it

Received 1 October 2008.

We prove that a maximal totally complex submanifold N2n of the quaternionic projective space HPn (n ≥ 2) is a parallel submanifold, provided that 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 U(n).

2000 Mathematics Subject Classification 53C26, 53C40, 53C28, 57S15, 53C29.


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