In this paper, we introduce Riemannian warped product submersions and construct examples and give fundamental geometric properties of such submersions. On the other hand, a necessary and sufficient condition for a Riemannian warped product submersion to be totally geodesic, totally umbilic and minimal is given.

中文翻译：

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黎曼翘曲积浸没

在本文中，我们介绍了黎曼翘曲积淹没并构造了示例并给出了这种淹没的基本几何特性。另一方面，给出了黎曼翘曲积浸没是完全测地线、完全脐带和最小的充要条件。