Geodesic
A Note on the Construction of Complex and Quaternionic Vector Fields on Spheres
Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 104-110

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A relationship between real, complex, and quaternionic vector fields on spheres is given by using a relationship between the corresponding standard inner products. The number of linearly independent complex vector fields on the standard $(4n-1)$-sphere is shown to be twice the number of linearly independent quaternionic vector fields plus $d$, where $d=1$ or $3$.
Keywords: complex vector field, quaternionic vector field, realification function, complexification function, James numbers. 
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     author = {M. Obiedat},
     title = {A {Note} on the {Construction} of {Complex} and {Quaternionic} {Vector} {Fields} on {Spheres}},
     journal = {Matemati\v{c}eskie zametki},
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M. Obiedat. A Note on the Construction of Complex and Quaternionic Vector Fields on Spheres. Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 104-110. http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a9/