On a product manifold ( M , r ), we consider four geometric structures compatible with r , e.g. hyper-paracomplex or bi-Lagrangian, and define distinguished generalized complex or paracomplex structures on M , which interpolate between some pairs of them. We study the twistor bundles whose smooth sections are these new structures, obtaining the typical fibers as homogeneous spaces of classical groups. Also, we give examples of product manifolds admitting some of these new structures.

中文翻译：

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乘积流形上的广义复数和超复数结构

在乘积流形 ( M , r ) 上，我们考虑与 r 兼容的四种几何结构，例如超超复复或双拉格朗日，并在 M 上定义区分的广义复或超复结构，在它们的某些对之间进行插值。我们研究了平滑截面是这些新结构的扭曲束，获得了作为经典群的齐次空间的典型纤维。此外，我们还给出了承认其中一些新结构的乘积流形的例子。