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Connections in the second order tangent bundle with extended structure group

Shurygin V.; Vashurina L. (2014)

© 2014, Pleiades Publishing, Ltd. The second order tangent bundle T2M of a smooth manifold M carries a natural structure of a smooth manifold over the algebra D2 of truncated polynomials of degree two in one variable, which ...
Holonomy Pseudogroup of a Manifold Over the Algebra of Dual Numbers and Some its Applications

Malyugina A.; Shurygin V. (2019)

© 2019, Allerton Press, Inc. 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 ...
Lie Jets and Higher-Order Partial Connections

Shurygin V.V. (2020)

© 2020, Springer Science+Business Media, LLC, part of Springer Nature. Higher-order partial connections are studied. We find conditions under which the Lie jet of a field of a geometric object ξ in the direction of the ...
Lifts of Poisson structures to Weil bundle

Shurygin V. (2012)

In the present paper, we study complete and vertical lifts of tensor fields from a smooth manifold M to its Weil bundle T AM defined by a Frobenius Weil algebra A. For a Poisson manifold (M, w), we show that the complete ...
On the higher order geometry of weil bundles over smooth manifolds and over parameter-dependent manifolds

Bushueva G.; Shurygin V. (2005)

The Weil bundle Tdouble-struck A signMn of an n-dimensional smooth manifold Mn determined by a local algebra double-struck A sign in the sense of A. Weil carries a natural structure of an n-dimensional A-smooth manifold. ...
Transverse Lie jets and holomorphic geometric objects on transverse bundles

Zubkova S.; Shurygin V. (2016)

© 2016, Allerton Press, Inc.Two holomorphic fields of geometric objects on a transverse Weil bundle are called equivalent if there exists a holomorphic diffeomorphism of this bundle onto itself which induces the identity ...

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