Mathematics – Differential Geometry
Scientific paper
2009-03-08
Mathematics
Differential Geometry
LaTeX2e, 31pages, explicit non quaternionic Kaehler structures with closed fundamental four form and new explicit Spin(7)-holo
Scientific paper
We construct explicit left invariant quaternionic contact structures on Lie groups with zero and non-zero torsion, and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of quaternionic contact manifolds not locally quaternionic contact conformal to the quaternionic sphere. We present a left invariant quaternionic contact structure on a seven dimensional non-nilpotent Lie group, and show that this structure is locally quaternionic contact conformal to the flat quaternionic contact structure on the quaternionic Heisenberg group. On the product of a seven dimensional Lie group, equipped with a quaternionic contact structure, with the real line we determine explicit complete quaternionic Kaehhler metrics and $Spin(7)$-holonomy metrics which seem to be new. We give explicit complete non-compact eight dimensional almost quaternion hermitian manifolds with closed fundamental four form which are not quaternionic K\"ahler.
de Andrés Luis C.
Fernández Marisa
Ivanov Stefan
Santisteban Jose A.
Ugarte Luis
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