Abstract:
It is known that for a vector field in three-dimensional space we can introduce the concepts of curvature and mean curvature. In the present article we derive integral formulas for these concepts; these formulas allow us to decide whether a vector field has, for example, singularities in a domain. We explain the influence of the modulus of the curvature of a vector field on the magnitude of its nonholonomity.
We also consider the question of the influence of the curvature of a family of surfaces on the distortion of the enveloping space for a given size of domain.
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