Topological properties of manifolds admitting a -Riemannian metric
Saved in:
| Title: | Topological properties of manifolds admitting a -Riemannian metric |
|---|---|
| Authors: | Chernov, Vladimir1 Vladimir.Chernov@dartmouth.edu, Kinlaw, Paul1 Paul.Kinlaw@dartmouth.edu, Sadykov, Rustam2 sadykov@math.toronto.edu |
| Source: | Journal of Geometry & Physics. Oct2010, Vol. 60 Issue 10, p1530-1538. 9p. |
| Subjects: | Topology, Riemannian manifolds, Geodesics, Fundamental groups (Mathematics), Homology theory, Hyperbolic spaces |
| Abstract: | Abstract: A complete Riemannian manifold is a -manifold if every unit speed geodesic originating at satisfies for . Bérard-Bergery proved that if is a -manifold, then is a closed manifold with finite fundamental group, and the cohomology ring is generated by one element. We say that is a -manifold if for every there exists such that for every unit speed geodesic originating at , the point is -close to . We use Low’s notion of refocussing Lorentzian space–times to show that if is a -manifold, then is a closed manifold with finite fundamental group. As a corollary we get that a Riemannian covering of a -manifold is a -manifold. Another corollary is that if is a -manifold, then is a -manifold for some metric . [Copyright &y& Elsevier] |
| Copyright of Journal of Geometry & Physics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 52224854 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Topological properties of manifolds admitting a -Riemannian metric – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Chernov%2C+Vladimir%22">Chernov, Vladimir</searchLink><relatesTo>1</relatesTo><i> Vladimir.Chernov@dartmouth.edu</i><br /><searchLink fieldCode="AR" term="%22Kinlaw%2C+Paul%22">Kinlaw, Paul</searchLink><relatesTo>1</relatesTo><i> Paul.Kinlaw@dartmouth.edu</i><br /><searchLink fieldCode="AR" term="%22Sadykov%2C+Rustam%22">Sadykov, Rustam</searchLink><relatesTo>2</relatesTo><i> sadykov@math.toronto.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Geometry+%26+Physics%22">Journal of Geometry & Physics</searchLink>. Oct2010, Vol. 60 Issue 10, p1530-1538. 9p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Topology%22">Topology</searchLink><br /><searchLink fieldCode="DE" term="%22Riemannian+manifolds%22">Riemannian manifolds</searchLink><br /><searchLink fieldCode="DE" term="%22Geodesics%22">Geodesics</searchLink><br /><searchLink fieldCode="DE" term="%22Fundamental+groups+%28Mathematics%29%22">Fundamental groups (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Homology+theory%22">Homology theory</searchLink><br /><searchLink fieldCode="DE" term="%22Hyperbolic+spaces%22">Hyperbolic spaces</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: A complete Riemannian manifold is a -manifold if every unit speed geodesic originating at satisfies for . Bérard-Bergery proved that if is a -manifold, then is a closed manifold with finite fundamental group, and the cohomology ring is generated by one element. We say that is a -manifold if for every there exists such that for every unit speed geodesic originating at , the point is -close to . We use Low’s notion of refocussing Lorentzian space–times to show that if is a -manifold, then is a closed manifold with finite fundamental group. As a corollary we get that a Riemannian covering of a -manifold is a -manifold. Another corollary is that if is a -manifold, then is a -manifold for some metric . [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Geometry & Physics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=52224854 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.geomphys.2010.05.010 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 9 StartPage: 1530 Subjects: – SubjectFull: Topology Type: general – SubjectFull: Riemannian manifolds Type: general – SubjectFull: Geodesics Type: general – SubjectFull: Fundamental groups (Mathematics) Type: general – SubjectFull: Homology theory Type: general – SubjectFull: Hyperbolic spaces Type: general Titles: – TitleFull: Topological properties of manifolds admitting a -Riemannian metric Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chernov, Vladimir – PersonEntity: Name: NameFull: Kinlaw, Paul – PersonEntity: Name: NameFull: Sadykov, Rustam IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2010 Type: published Y: 2010 Identifiers: – Type: issn-print Value: 03930440 Numbering: – Type: volume Value: 60 – Type: issue Value: 10 Titles: – TitleFull: Journal of Geometry & Physics Type: main |
| ResultId | 1 |
