Geodesic
Sources of curvature of a~vector field
Sbornik. Mathematics, Tome 9 (1969) no. 2, pp. 199-211

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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. Bibliography: 5 titles. 
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     author = {Yu. A. Aminov},
     title = {Sources of curvature of a~vector field},
     journal = {Sbornik. Mathematics},
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     number = {2},
     year = {1969},
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     url = {http://geodesic.mathdoc.fr/item/SM_1969_9_2_a4/}
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Yu. A. Aminov. Sources of curvature of a~vector field. Sbornik. Mathematics, Tome 9 (1969) no. 2, pp. 199-211. http://geodesic.mathdoc.fr/item/SM_1969_9_2_a4/