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- W1699168559 abstract "Abstract — Let M be an almost split quaternionic manifold on which its almost split quaternionic structure is defined by a three dimensional subbundle V of TM T M () () ∗⊗ and {} FG H ,, be a local basis for V . Suppose that the (global) ( 1, 2 ) tensor field defined [ VV , ] is defined by [ VV FF GG H H ,, , , ] =+ + [ ] [ ] [ ] , where [ , ] denotes the Nijenhuis bracket. In ref. [7], for the almost split-hypercomplex structure H == Jα ,1,2,3α , and the Obata connection ∇H vanishes if and only if H is split-hypercomplex. In this study, we give a prof, in particular, prove that if either M is a split quaternionic Kaehler manifold, or if M is a split-complex manifold with almost split-complex structure F , then the vanishing [ VV , ] is equivalent to that of all the Nijenhuis brackets of {} FG H ,, . It follows that the bundle V is trivial if and only if [ VV , ] =0 . Keywords — Almost split - hypercomplex structure, Almost split quaternionic structure, Almost split quaternion Kaehler manifold, Obata connection." @default.
- W1699168559 created "2016-06-24" @default.
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- W1699168559 date "2008-07-28" @default.
- W1699168559 modified "2023-10-18" @default.
- W1699168559 title "A Global Condition for the Triviality of an Almost Split Quaternionic Structure on Split Complex Manifolds" @default.
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