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TitleQuaternionic Heisenberg groups as naturally reductive homogeneous spaces
Author(s)Ferreira, Ana Cristina
Agricola, Ilka
Storm, Reinier
KeywordsQuaternionic Heisenberg groups
naturally reductive homogeneous spaces
generalized Killing spinors
Issue dateMay-2015
PublisherWorld Scientific Publishing
JournalInternational Journal of Geometric Methods in Modern Physics
Abstract(s)In this paper, we describe the geometry of the quaternionic Heisenberg groups from a Riemannian viewpoint. We show, in all dimensions, that they carry an almost 3- contact metric structure which allows us to define the metric connection that equips these groups with the structure of a naturally reductive homogeneous space. It turns out that this connection, which we shall call the canonical connection because of its analogy to the 3-Sasaki case, preserves the horizontal and vertical distributions and even the quaternionic contact (qc) structure of the quaternionic Heisenberg groups. We focus on the 7-dimensional case and prove that the canonical connection can also be obtained by means of a cocalibrated G2 structure. We then study the spinorial properties of this group and present the noteworthy fact that it is the only known example of a manifold which carries generalized Killing spinors with three different eigenvalues.
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AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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