Results 31 to 40 of about 292,639 (308)
Discrete connections on principal bundles: abelian group case
, 2021 In this note we consider a few interesting properties of discrete connections on principal bundles when the structure group of the bundle is an abelian Lie group. In particular, we show that the discrete connection form and its curvature can be interpreted as singular $1$ and $2$ cochains respectively, with the curvature being the coboundary of the ...
Fernandez, Javier +2 more
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Linear and projective connections over a smooth manifold
Дифференциальная геометрия многообразий фигур, 2023 The principal bundles of the first order coframes and the second order coframes, as well as factor bundle of centroprojective (coaffine) coframes are considered.
Yu. I. Shevchenko, A. V. Vyalova
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Дифференциальная геометрия многообразий фигур, 2020 The hypercentered planes family, whose dimension coincides with dimension of generating plane, is considered in the projective space. Two principal fiber bundles arise over it.
A.V. Vyalova
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Glued linear connection on surface of the projective space
Дифференциальная геометрия многообразий фигур, 2020 We consider a surface as a variety of centered planes in a multidimensional projective space. A fiber bundle of the linear coframes appears over this manifold. It is important to emphasize the fiber bundle is not the principal bundle.
K.V. Bashashina
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Дифференциальная геометрия многообразий фигур, 2021 In n-dimensional projective space Pn a manifold , i. e., a family of pairs of planes one of which is a hyperplane in the other, is considered. A principal bundle arises over it, . A typical fiber is the stationarity subgroup of the generator of pair of
A.V. Vyalova, Yu. I. Shevchenko
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The composition equipment for congruence of hypercentred planes
Дифференциальная геометрия многообразий фигур, 2019 In n-dimensional projective space Pn a manifold , i. e., a congruence of hypercentered planes , is considered. By a hypercentered planе we mean m-dimensional plane with a (m – 1)-dimensional hyperplane , distinguished in it.
A. V. Vyalova
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Сurvature-torsion tensor for Cartan connection
Дифференциальная геометрия многообразий фигур, 2019 A Lie group containing a subgroup is considered. Such a group is a principal bundle, a typical fiber of this principal bundle is the subgroup and a base is a homogeneous space, which is obtained by factoring the group by the subgroup.
Yu. Shevchenko
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A remark on “Connections and Higgs fields on a principal bundle” [PDF]
Annals of Global Analysis and Geometry, 2011 We show that a unipotent vector bundle on a non-Kaehler compact complex manifold does not admit a flat holomorphic connection in general. We also construct examples of topologically trivial stable vector bundle on compact Gauduchon manifold that does not admit any unitary flat connection.
Carlos Florentino, Indranil Biswas
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he deformation pseudotensor of connections in cocongruence K (n - m)m
Дифференциальная геометрия многообразий фигур, 2023 The Grassmann manifold is the set of all -dimensional planes of an -dimensional projective space, with dim. One of the submanifolds of the Grassmann manifold is a complex of -planes if the dimension of the complex exceeds the difference .
O. O. Belova
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Induced connections of two types on a surface of an affine space
Дифференциальная геометрия многообразий фигур, 2019 In the affine space the fundamental-group connection in the bundle associated with a surface as a manifold of tangent planes is investigated. The principal bundle contains a quotient bundle of tangent frames, the typical fiber of which is a linear group ...
A. Shults
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