@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}, }