Our aim is to support the choice of two remarkable connections with torsion in a 3-Sasakian manifold, proving that, in contrast to the Levi-Civita connection, the holonomy group in the homogeneous cases reduces to a proper subgroup of the special orthogonal group, of dimension considerably smaller. We realize the computations of the holonomies in a unified way, by using as a main algebraic tool a nonassociative structure, that of a symplectic triple system.

中文翻译：

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完整和3-Sasakian同质流形与辛三重系统

我们的目标是支持在3-Sasakian流形中选择两个具有扭转关系的显着连接，证明与Levi-Civita连接不同，均质情况下的完整性组减少到特殊正交组的适当子组，尺寸要小得多。通过使用非三元系统的非缔合结构作为主要代数工具，我们以统一的方式实现了完整的整数计算。