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 $\mathbb{H}{\mathbb{P}}^n$ ($n\ge 2$) 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 $\mathrm{U}(n)$.

15 pages

References in corpus (1)

• A Berger type normal holonomy theorem for complex submanifolds

Cited by in corpus (1)

• Calibrated Geometry in Hyperkahler Cones, 3-Sasakian Manifolds, and Twistor Spaces