Corpus ID: 199551924

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

@article{Martins2019ExistenceO,
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},
year={2019}
}
• Published 13 August 2019
• Mathematics
• 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, $\Gamma… Expand 1 Citations Geometric Regularity Results on$B_{\alpha,\beta}^{k}$-Manifolds, I: Affine Connections • Mathematics • 2020 In this paper we consider the existence problem of affine connections on$C^{k}$-manifolds$M$whose coefficients are as regular as one needs. We show that if$M$admits a suitable subatlas, meaningExpand #### References SHOWING 1-10 OF 21 REFERENCES Every conformal class contains a metric of bounded geometry • Mathematics • 2015 We show that on every manifold, every conformal class of semi-Riemannian metrics contains a metric $$g$$g such that each $$k$$kth-order covariant derivative of the Riemann tensor of $$g$$g hasExpand Convenient Categories of Smooth Spaces • Mathematics • 2008 A "Chen space" is a set X equipped with a collection of "plots" - maps from convex sets to X - satisfying three simple axioms. While an individual Chen space can be much worse than a smooth manifold,Expand Embeddings and immersions Preface to the English edition Preface Regular closed curves in the plane$C^r$manifolds,$C^r$maps, and fiber bundles Embeddings of$C^\infty$manifolds Immersions of$C^\infty\$ manifolds TheExpand
∞-Categories for the Working Mathematician
homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition,Expand
Monoidal Functors, Species, and Hopf Algebras
• Mathematics
• 2010
This research monograph integrates ideas from category theory, algebra and combinatorics. It is organised in three parts. Part I belongs to the realm of category theory. It reviews some of theExpand
Handbook of Categorical Algebra
The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic ofExpand
Complex analytic connections in fibre bundles
Introduction. In the theory of differentiable fibre bundles, with a Lie group as structure group, the notion of a connection plays an important role. In this paper we shall consider complex analyticExpand
Models for smooth infinitesimal analysis
• Mathematics
• 1990
The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques ofExpand
Symplectic connections
• Mathematics
• 2005
This article is an overview of the results obtained in recent years on symplectic connections. We present what is known about preferred connections (critical points of a variational principle). TheExpand
Connections withLP bounds on curvature
We show by means of the implicit function theorem that Coulomb gauges exist for fields over a ball inRn when the integralLn/2 field norm is sufficiently small. We then are able to prove a weakExpand