This paper presents an investigation of the relation between some positivity of the curvature and the finiteness of fundamental groups in semi-Riemannian geometry. We consider semi-Riemannian submersions $\pi : (E, g) \to (B, -g_B)$ under the condition with $(B, g_B)$ Riemannian, the fiber closed Riemannian, and the horizontal distribution integrable. Then we prove that, if the lightlike geodesically complete or timelike geodesically complete semi-Riemannian manifold $E$ has some positivity of curvature, then the fundamental group of the fiber is finite. Moreover we construct an example of semi-Riemannian submersions with some positivity of curvature, non-integrable horizontal distribution, and the finiteness of the fundamental group of the fiber.

中文翻译：

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具有正曲率张量的半黎曼流形的基本群

本文研究了半黎曼几何中曲率的某些正性与基本群的有限性之间的关系。我们考虑半黎曼淹没 $\pi : (E, g) \to (B, -g_B)$ 在 $(B, g_B)$ 黎曼函数、纤维闭合黎曼函数和水平分布可积的条件下。然后我们证明，如果类光测地完全或类时间测地完全半黎曼流形$E$具有一定的曲率正性，则纤维的基本群是有限的。此外，我们构建了一个半黎曼浸没的例子，它具有一定的曲率正性、不可积的水平分布和纤维基本群的有限性。