Geodesic
Holonomy pseudogroup of a manifold over the algebra of dual numbers and some its applications
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2019), pp. 82-88.

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We study properties of the holonomy pseudogroup on a total immersed transversal of the canonical foliation on a smooth manifold over the algebra of dual numbers $\mathbb{D}$. We apply holonomy pseudogroups to the investigation of $\mathbb{D}$-diffeomorphisms between quotient manifolds of the algebra $\mathbb{D}$ by lattices and between $\mathbb{D}$-smooth manifolds naturally associated with an affine manifold.
Keywords: affine manifold, manifold over the algebra of dual numbers, foliated bundle, tangent bundle, tangent manifold, torus over the algebra of dual numbers, Weil bundle.
Mots-clés : foliation 
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A. A. Malyugina; V. V. Shurygin. Holonomy pseudogroup of a manifold over the algebra of dual numbers and some its applications. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2019), pp. 82-88. http://geodesic.mathdoc.fr/item/IVM_2019_2_a8/

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