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QUANTITATIVE DARBOUX THEOREMS IN CONTACT GEOMETRY.
- Source :
-
Transactions of the American Mathematical Society . Nov2016, Vol. 368 Issue 11, p7845-7881. 37p. - Publication Year :
- 2016
-
Abstract
- This paper begins the study of relations between Riemannian geometry and contact topology on (2n + 1)-manifolds and continues this study on 3-manifolds. Specifically we provide a lower bound for the radius of a geodesic ball in a contact (2n+ 1)-manifold (M, ξ) that can be embedded in the standard contact structure on R2n+1, that is, on the size of a Darboux ball. The bound is established with respect to a Riemannian metric compatible with an associated contact form a for ξ. In dimension 3, this further leads us to an estimate of the size for a standard neighborhood of a closed Reeb orbit. The main tools are classical comparison theorems in Riemannian geometry. In the same context, we also use holomorphic curve techniques to provide a lower bound for the radius of a PS-tight ball. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 368
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 118197298
- Full Text :
- https://doi.org/10.1090/tran/6821