Corpus ID: 199551924

Existence of $B^k_{\alpha,\beta}$-Structures on $C^k$-Manifolds.

  title={Existence of \$B^k\_\{\alpha,\beta\}\$-Structures on \$C^k\$-Manifolds.},
  author={Y. X. Martins and Rodney Josu'e Biezuner},
  journal={arXiv: Differential Geometry},
In this paper we introduce $B_{\alpha,\beta}^{k}$-manifolds as generalizations of the notions of smooth manifolds with $G$-structure or with $k$-bounded geometry. These are $C^{k}$-manifolds whose transition functions $\varphi_{ji}=\varphi_{j}\circ\varphi_{i}^{-1}$ are such that $\partial^{\mu}\varphi_{ji}\in B_{\alpha(r)}\cap C^{k-\beta(r)}$ for every $\vert\mu\vert=r$, where $B=(B_{r})_{r\in\Gamma}$ is some sequence of presheaves of Frechet spaces endowed with further structures, $\Gamma… Expand
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