Pseudo-Riemannian Foliations and Their Graphs
- Autores: Dolgonosova A.1, Zhukova N.1
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Afiliações:
- Department of Informatics, Mathematics and Computer Sciences
- Edição: Volume 39, Nº 1 (2018)
- Páginas: 54-64
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/200850
- DOI: https://doi.org/10.1134/S1995080218010092
- ID: 200850
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Resumo
We prove that a foliation (M,F) of codimension q on a n-dimensional pseudo-Riemannian manifold with induced metrics on leaves is pseudo-Riemannian if and only if any geodesic that is orthogonal at one point to a leaf is orthogonal to every leaf it intersects. We show that on the graph G = G(F) of a pseudo-Riemannian foliation there exists a unique pseudo-Riemannian metric such that canonical projections are pseudo-Riemannian submersions and the fibers of different projections are orthogonal at common points. Relatively this metric the induced foliation (G, F) on the graph is pseudo-Riemannian and the structure of the leaves of (G, F) is described. Special attention is given to the structure of graphs of transversally (geodesically) complete pseudo-Riemannian foliations which are totally geodesic pseudo-Riemannian ones.
Sobre autores
A. Dolgonosova
Department of Informatics, Mathematics and Computer Sciences
Autor responsável pela correspondência
Email: annadolgonosova@gmail.com
Rússia, ul. Myasnitskaya 20, Moscow, 101000
N. Zhukova
Department of Informatics, Mathematics and Computer Sciences
Email: annadolgonosova@gmail.com
Rússia, ul. Myasnitskaya 20, Moscow, 101000