Locally convex surfaces immersed in a Killing submersion
Locally convex surfaces immersed in a Killing submersion
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局部凸面沉浸在致命的浸没中
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
I. S. D. Oliveira
中科院分区：
文献类型：
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作者：
J. Espinar;I. S. D. Oliveira
我们将Hadamard- stoker - currier定理推广到在严格Hadamard曲面上的沈浸曲面，其纤维是单位沈浸场的轨迹。我们证明了在每个点上主曲率大于某个函数（取决于周围流形）的每一个完备曲面，必须是适当嵌入的，与球面或平面同胚，在后者的情况下，我们研究了端点的行为。
We generalize Hadamard-Stoker-Currier Theorems for surfaces immersed in a Killing submersion over a strictly Hadamard surface whose fibers are the trajectories of a unit Killing field. We prove that every complete surface whose principal curvatures are greater than a certain function (depending on the ambient manifold) at each point, must be properly embedded, homeomorphic either to the sphere or to the plane and, in the latter case, we study the behavior of the end.