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arXiv · 1203.3690

On the geometry of the orbits of Killing vector fields

A. Ya. Narmanov·J. O. Aslonov
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Abstract

Let $D$ be a set of smooth vector fields on the smooth manifold $M$.It is known that orbits of $D$ are submanifolds of M. Partition $F$ of M into orbits of $D$ is a singular foliation. In this paper we are studying geometry of foliation which is generated by orbits of a family of Killing vector fields.In the case $M=R^3$ it is obtained full geometrical classification of $F$. Throughout this paper the word "smooth" refers to a class $C^\infty$.

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A. Ya. Narmanov, J. O. Aslonov. 2012-03-16. On the geometry of the orbits of Killing vector fields. https://arxiv.org/abs/1203.3690

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