arXiv subjects

A. Ya. Narmanov

Publications and source records attributed to A. Ya. Narmanov.

2 recordsLinked to original sources

arXiv2012

Foliation Theory and it's applications

Subject of present paper is the review of results of authors on foliation theory and applications of foliation theory in control systems. The paper consists of two parts. In the first part the results of authors on foliation theory are presented, in the second part the results on applications of foliation theory in the qualitative theory of control systems are given. In paper everywhere smoothness of a class $C^\infty$ is considered.

math.DG↗

arXiv2012

On the geometry of the orbits of Killing vector fields

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 $C^\infty$.

math.DG↗