Mutual compositions in even-dimensional affinely connected space without a torsion

Consider an affinely connected space without a torsion A2n. [6] introduces pairs of mutual compositions Xn x X n and Yn x Y n , defined by the afinors aa and ba . This paper considers two new compositions given by the affinors a = V2 (aa + ba ) and Ca = V2 (aa - ba ). We show that these compositions define integrable structures in A2n .