论文标题
伪里曼尼亚歧管的显式等距嵌入：思想和应用
Explicit isometric embeddings of pseudo-Riemannian manifolds: ideas and applications
论文作者
论文摘要
我们研究了（伪） - 里曼尼亚歧管的显式等距嵌入的构建问题。我们讨论了基于嵌入式表面的外部对称性和公制的内部对称性必须相同的想法的方法。如果具有足够高的公制对称性，则这种方法允许转换度量诱导性条件，该条件是为了构建嵌入的ODES系统而要解决的方法。事实证明，只要发生上述简化，该方法就可以概括为允许表面具有较低的对称性。这种概括可以用于构建对称组的指标嵌入，以及用于构建异米法变形（弯曲）表面的指标。我们举例说明了这种方法的应用。特别是，我们构建了与Godel Universe相连的球体，三孔和挤压广告宇宙的空间燃料弗里德曼模型和等距弯曲的嵌入。
We study the problem of construction of explicit isometric embeddings of (pseudo)-Riemannian manifolds. We discuss the method which is based in the idea that the exterior symmetry of the embedded surface and the interior symmetry of the metric on it must be the same. In case of high enough symmetry of the metric such method allows to transform the metric inducedness condition, which is the one to be solved in order to construct an embedding, into a system of ODEs. It turns out that this method can be generalized to allow the surface to have lower symmetry as long as the above simplification occurs. This generalization can be of use in the construction of embeddings for metrics whose symmetry group is hard to analyze, as well for the construction of isometrically deformed (bended) surface. We give some examples of application of this method. In particular, we construct the embedding of spatially-flat Friedmann model and isometric bendings of sphere, 3-sphere and squashed AdS universe, which is connected to the Godel universe.
