Every conformal class contains a metric of bounded geometry
| Autor: | Müller, Olaf, Nardmann, Marc |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Mathematische Annalen 363 (2015), 143-174 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00208-014-1162-z |
| Popis: | We show that on every manifold, every conformal class of semi-Riemannian metrics contains a metric $g$ such that each $k$-th-order covariant derivative of the Riemann tensor of $g$ has bounded absolute value $a_k$. This result is new also in the Riemannian case, where one can arrange in addition that $g$ is complete with injectivity and convexity radius greater than 1. One can even make the radii rapidly increasing and the functions $a_k$ rapidly decreasing at infinity. We prove generalizations to foliated manifolds, where curvature, second fundamental form and injectivity radius of the leaves can be controlled similarly. Moreover, we explain a general principle that can be used to obtain analogous results for Riemannian manifolds equipped with arbitrary other additional geometric structures instead of foliations. Comment: 22 pages, 1 figure. The journal article differs from this version only by marginal adaptations required by the publisher's style guidelines, and by one minor typo |
| Databáze: | arXiv |
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