2003/04/27 by Srdjan Vukmirovic, Vukmirovic, Srdjan
Mathematics · #53C07 #53C15 #53C80 #53G10 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C07 #msc:53C15 #msc:53C80 #msc:53G10
paper · pdf · doi:10.48550/arxiv.math/0304424
21 page
arxiv created 2003/04/27 · arxiv updated 2009/11/30
The pseudo-Riemannian manifold M=(M4n,g), n ≥ 2 is para-quaternionic K" ahler if hol(M) ⊂ sp(n, \RR) ⊕ sp(1, \RR). If hol(M) ⊂ sp(n, \RR), than the manifold M is called para-hyperK" ahler. 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 K" ahler and para-hyperK" ahler manifolds and give some examples. The decomposition of a curvature tensor of the para-quaternionic type is also described.