论文标题
克莱拉特共同淹没
Clairaut Conformal Submersions
论文作者
论文摘要
本文的目的是在里曼尼亚人的流形之间介绍克莱拉特的形成糊状。首先，我们发现保形淹没是克拉拉特·综合淹没的必要条件。特别是，我们在共形浸入的总歧管上获得了Geodesics的Clairaut关系，并证明Clairaut保形浸入其纤维沿其纤维完全扩张，这完全是脐带，平均曲率是功能的梯度。此外，我们计算总歧管的垂直分布的标量和RICCI曲率。此外，我们发现Clairaut共形淹没是谐波的必要条件。对于克莱拉特（Clairaut）串扰，我们发现该度量标准在其域或图像上的共形变化，这些变化赋予了克莱拉特·里曼尼（Clairaut Riemannian）浸没，克莱拉特（Clairaut）的clairaut sonformal浸入，带有完全地理素质的纤维或谐波克莱拉特浸没。最后，我们给出了两个非平凡的示例，以说明这一理论，并提出每个克莱拉特综合淹没的局部模型，并具有可整合的水平分布。
The aim of this paper is to introduce Clairaut conformal submersions between Riemannian manifolds. First, we find necessary and sufficient conditions for conformal submersions to be Clairaut conformal submersions. In particular, we obtain Clairaut relation for geodesics on the total manifolds of conformal submersions, and prove that Clairaut conformal submersions have constant dilation along their fibers, which are totally umbilical, with mean curvature being gradient of a function. Further, we calculate the scalar and Ricci curvatures of the vertical distributions of the total manifolds. Moreover, we find a necessary and sufficient condition for Clairaut conformal submersions to be harmonic. For a Clairaut conformal submersion we find conformal changes of the metric on its domain or image, that give a Clairaut Riemannian submersion, a Clairaut conformal submersion with totally geodesic fibers, or a harmonic Clairaut submersion. Finally, we give two non-trivial examples of Clairaut conformal submersions to illustrate the theory and present a local model of every Clairaut conformal submersion with integrable horizontal distribution.
