Holonomy Pseudogroup of a Manifold Over the Algebra of Dual Numbers and Some its Applications
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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 ⅅ. We apply holonomy pseudogroups to the investigation of ⅅ-diffeomorphisms between quotient manifolds of the algebra ⅅ by lattices and between ⅅ-smooth manifolds naturally associated with an affine manifold.
Keywordsaffine manifold manifold over the algebra of dual numbers foliation foliated bundle tangent bundle tangent manifold torus over the algebra of dual numbers Weil bundle
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