ON THE COMMUTING KILLING VECTOR FIELDS ON THE SPHERES SAITOVA SAYYORA

The Killing vector fields are the most important vector fields in numeric areas of differential geometry, qualitative control theory and physics, as they generate the group action of isometries on the smooth manifolds and the geometry of their orbits represents the attainability sets of the family of Killing vector fields on the manifolds. Using the properties of Killing vector fields in Euclidian spaces we investigate orbits of the family of Killing vector fields on the spheres. According to conditions of a given family we can define types of the orbits and properties of covariant differential along given Killing vector fields.