Abstract
When the four-dimensional Euclidean space is endowed with a covariant derivative that is either self-dual or antiself-dual and of constant curvature, the corresponding magnetic Laplacian is closely related to the sub-Laplacian of the quaternionic Heisenberg group. Some geometric properties of this operator are studied. In particular, it is proved that there exists a canonical orthogonal complex structure which provides a factorization in the sense of Schrödinger.
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