Totally umbilical hypersurfaces of manifolds admitting a unit Killing field
Totally umbilical hypersurfaces of manifolds admitting a unit Killing field
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接纳一个单元的流形的完全脐超曲面 杀伤场
DOI：
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发表时间：
2010
期刊：
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通讯作者：
J. Veken
中科院分区：
文献类型：
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作者：
Rabah Souam;J. Veken
证明了M × R型黎曼积（R为欧氏线）当且仅当M具有局部翘曲积的结构时存在完全脐带超曲面，并给出了这种情况下完全脐带超曲面的完整描述。此外，我们给出了带有单位杀戮场的黎曼三流形允许完全测地线面的充分必要条件，并研究了满足该条件的三流形的局部和全局性质。
We prove that a Riemannian product of type M x R (where R denotes the Euclidean line) admits totally umbilical hypersurfaces if and only if M has locally the structure of a warped product and we give a complete description of the totally umbilical hypersurfaces in this case. Moreover, we give a necessary and sufficient condition under which a Riemannian three-manifold carrying a unit Killing field admits totally geodesic surfaces and we study local and global properties of three-manifolds satisfying this condition.