Geodesic
Nonholonomic torses of the first kind
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2012), pp. 51-61

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In the three-dimensional Euclidean space we study two-dimensional nonholonomic distributions of planes orthogonal to a vector field with zero total curvature of the first kind (they are called nonholonomic torses of the first kind). Using the Cartan method [1] and a canonical moving frame, we study geometric properties of two kinds: 1) one of the principal curvatures of the first kind differs from zero (the general case); 2) both principal curvatures of the first kind equal zero (a nonholonomic plane). The result in case 2) is obtained in a general form.
Keywords: nonholonomic geometry, vector field.
Mots-clés : distribution, Pfaff equation 
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     author = {O. V. Tsokolova},
     title = {Nonholonomic torses of the first kind},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {51--61},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_3_a6/}
}
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O. V. Tsokolova. Nonholonomic torses of the first kind. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2012), pp. 51-61. http://geodesic.mathdoc.fr/item/IVM_2012_3_a6/