• Corpus ID: 203902760

Geometric Regularity Results on $B_{\alpha,\beta}^{k}$-Manifolds, I: Affine Connections

@article{Martins2020GeometricRR,
  title={Geometric Regularity Results on \$B\_\{\alpha,\beta\}^\{k\}\$-Manifolds, I: Affine Connections},
  author={Yuri Ximenes Martins and Rodney Josu'e Biezuner},
  journal={arXiv: Differential Geometry},
  year={2020}
}
In this paper we consider the existence problem of affine connections on $C^{k}$-manifolds $M$ whose coefficients are as regular as one needs. We show that if $M$ admits a suitable subatlas, meaning a $\mathcal{B}_{\alpha,\beta}^{k}$-structure for a certain presheaf of Fr\'echet spaces $B$ and for certain functions $\alpha$ and $\beta$, then the existence of such regular connections can be established. It is also proved that if the $\mathcal{B}_{\alpha,\beta}^{k}$-structure is actually nice (in… 

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