On the classification of Killing submersions and their isometries
On the classification of Killing submersions and their isometries
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论杀伤沉没的分类及其等轴性
DOI：
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发表时间：
2012
期刊：
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通讯作者：
J. M. Manzano
中科院分区：
文献类型：
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作者：
J. M. Manzano
Killing浸没是从可定向三维流形到可定向曲面的黎曼浸没，该曲面的纤维是三维流形中单位Killing向量场的积分曲线。我们对单连通黎曼曲面上的所有Killing淹没进行了分类，并给出了许多Killing淹没的显式模型，包括单连通常高斯曲率曲面上的Killing淹没。我们还充分描述了保持垂直方向的全空间的等距。因此，我们证明了只有E（k，t）-空间才是具有Killing淹没结构的单连通齐性三维流形，其等距群的维数至少为4。
A Killing submersion is a Riemannian submersion from an orientable 3-manifold to an orientable surface whose fibers are the inte- gral curves of a unit Killing vector field in the 3-manifold. We classify all Killing submersions over simply-connected Riemannian surfaces and give explicit models for many Killing submersions including those over simply-connected constant Gaussian curvature surfaces. We also fully describe the isometries of the total space preserving the vertical direc- tion. As a consequence, we prove that the only simply-connected homo- geneous 3-manifolds which admit a structure of Killing submersion are the E(k,t)-spaces, whose isometry group has dimension at least 4.