We prove that a maximal totally complex 2n-dimensional submanifold N of the quaternionic projective space HP(n) (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).
Maximal totally complex submanifolds of HP^n : homogeneity and normal holonomy / F. PODESTA'; L. BEDULLI; A. GORI. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - STAMPA. - 41:(2009), pp. 1029-1040. [10.1112/blms/bdp081]
Maximal totally complex submanifolds of HP^n : homogeneity and normal holonomy
PODESTA', FABIO;
2009
Abstract
We prove that a maximal totally complex 2n-dimensional submanifold N of the quaternionic projective space HP(n) (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).
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