WASET
	@article{(Open Science Index):https://publications.waset.org/pdf/3292,
	  title     = {A Global Condition for the Triviality of an Almost Split Quaternionic Structure on Split Complex Manifolds},
	  author    = {Erhan Ata and  Yusuf Yaylı},
	  country	= {},
	  institution	= {},
	  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 ( 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 .},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {2},
	  number    = {7},
	  year      = {2008},
	  pages     = {466 - 470},
	  ee        = {https://publications.waset.org/pdf/3292},
	  url   	= {https://publications.waset.org/vol/19},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 19, 2008},
	}