We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invariant submersion to be a totally geodesic map. Finally, we study semi-invariant submersions with totally umbilical fibers.

中文翻译：

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来自近 Kaehler 流形的半不变黎曼浸没

我们研究了从近凯勒流形到黎曼流形的半不变黎曼浸没。众所周知，黎曼淹没的垂直分布总是可积的，因此，我们推导了半不变黎曼淹没的水平分布的可积条件，并研究了叶理的几何形状。我们讨论了半不变淹没的存在和不存在，使得总流形是通常的乘积流形或扭曲的乘积流形。我们建立了半不变浸没成为完全测地线图的充要条件。最后，我们研究了完全脐纤维的半不变浸没。