EXISTENCE OF QUASI-DOUBLE LINES OF THE PAIR OF FOUR DIMENSIONAL DISTRIBUTIONS IN PARTIAL MAPPING OF EUCLIDEAN SPACE
DOI:
https://doi.org/10.52754/16948645_2024_2(5)_17Keywords:
partial mapping, Frenet’s frame, Euclidean space, distribution, cyclic net of Frenet, quasi-double lineAbstract
A family of smooth lines given in the domain so that through each point passes one line of given family. A movable frame is chosen so that it was Frenet’s frame for the line of the given family. The integral lines of the coordinate vectors fields of this frame form a Frenet’s net. On a tangent to the line a point is defined in an invariant way. When the point moves in the domain , the point describes it's domain In this way we get a partial mapping such, that .
It is considered the four dimensional distributions and . It is found the necessary and sufficient conditions for lines and to be quasi-double lines of the pair of distributions in the partial mapping
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