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Mathematics > Differential Geometry

arXiv:2206.00336 (math)
[Submitted on 1 Jun 2022 (v1), last revised 14 Mar 2023 (this version, v2)]

Title:Formal frames and deformations of affine connections

Authors:Taro Asuke
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Abstract:We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a generalization of the structural equations. It will be shown that the vanishing of torsions are equivalent to the realizability of given formal frames as ordinary frames. We will also discuss deformations of linear connections on tangent bundles. An application to deformations of foliations are then given.
Comments: A remark and a reference added
Subjects: Differential Geometry (math.DG)
MSC classes: Primary 53B05, Secondary 58A20, 58H15, 57R32, 57R20
Cite as: arXiv:2206.00336 [math.DG]
  (or arXiv:2206.00336v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.2206.00336

Submission history

From: Taro Asuke [view email]
[v1] Wed, 1 Jun 2022 08:57:45 UTC (25 KB)
[v2] Tue, 14 Mar 2023 12:28:33 UTC (25 KB)
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