On the geometry of the orbits of Killing vector fields

Details On the geometry of the orbits of Killing vector fields On the geometry of the orbits of Killing vector fields

2012-03-16

arxiv.org/abs/1203.3690v1

Mathematics

Differential Geometry

6 pages

Scientific paper

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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