Quaternionic Reduction
نویسنده
چکیده
The pseudo-Riemannian manifold M = (M, g), n ≥ 2 is paraquaternionic Kähler if hol(M) ⊂ sp(n,R)⊕sp(1, R). If hol(M) ⊂ sp(n, R), than the manifold M is called para-hyperKähler. The other possible definitions of these manifolds use certain parallel para-quaternionic structures in End(TM), similarly to the quaternionic case. In order to relate these different definitions we study para-quaternionic algebras in details. We describe the reduction method for the para-quaternionic Kähler and para-hyperKähler manifolds and give some examples. The decomposition of a curvature tensor of the paraquaternionic type is also described.
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