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Pré-Publication, Document De Travail Année : 2020

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

Résumé

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 the sense of arXiv:1908.04442), then a multiplicity result can also be obtained by means of Thom's transversality arguments.
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Dates et versions

hal-02907902 , version 1 (27-07-2020)
hal-02907902 , version 2 (06-02-2021)

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Yuri Ximenes Martins, Rodney Josué Biezuner. Geometric Regularity Results on $B_{\alpha,\beta}^{k}$-Manifolds, I: Affine Connections. 2020. ⟨hal-02907902v1⟩
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