Abstract:The geometry of orbits of families of smooth vector fields was studied by many mathematicians due
to its importance in applications in the theory of control systems, in dynamic systems, in geometry
and in the theory of foliations.
In this paper it is studied geometry of orbits of vector fields in four dimensional Euclidean space. It is shown that orbits generate
singular foliation every regular leaf of which is a surface of negative Gauss curvature and zero normal torsion.
In addition, the invariant function… Show more
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