ON A PARTIAL MAPPING OF EUCLIDIAN SPACE GENERATED BY A GIVEN DISTRIBUTION

Abstract

 In this paper, research is carried out on the partial mapping of Euclidean space generated by a given distribution. It is considered a three dimensional distribution  in domain of Euclidean space .Then it is defined a orthogonal-complimentary distribution to given distribution by invariant way. By the vectors of mean curvatures of these distributions we define a partial mapping of the space  and investigate this partial mapping. It is proved necessary and sufficient conditions of minimality of the images of distributions  and   in the partial mapping of the Euclidean space . It is found out of the geometrical meaning of the final equations. The necessary and sufficient conditions for the minimality of distribution images in a partial mapping are found  .