%0 Journal Article
	%A Erhan Ata and  Yusuf Yaylı
	%D 2008
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 19, 2008
	%T A Global Condition for the Triviality of an Almost Split Quaternionic Structure on Split Complex Manifolds
	%U https://publications.waset.org/pdf/3292
	%V 19
	%X Let M be an almost split quaternionic manifold on
which its almost split quaternionic structure is defined by a three
dimensional subbundle V of ( T M) T (M)
*
Ôèù and
{F,G,H} be a local basis for V . Suppose that the (global)
(1, 2) tensor field defined[V ,V ]is defined by
[V,V ] = [F,F]+[G,G] + [H,H], where [,] denotes
the Nijenhuis bracket. In ref. [7], for the almost split-hypercomplex
structureH = J α,α =1,2,3, and the Obata
connection ÔêçH
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 splitcomplex
manifold with almost split-complex structure F , then the
vanishing [V ,V ] is equivalent to that of all the Nijenhuis brackets
of {F,G,H}. It follows that the bundle V is trivial if and only if
[V ,V ] = 0 .
	%P 466 - 470