Associated Metrics for Bourgeois’ Contact Forms
In 2002, Frédéric Bourgeois [2] showed that, given a compact contact manifold M 2n–1, the product M 2n–1 × T 2 also carries a contact form; then, as a corollary he observed that all odd-dimensional tori have contact forms. The idea is to use an open book decomposition of M 2n–1 that is compatible wi...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2019-11-01
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| Series: | Memoirs of the Scientific Sections of the Romanian Academy |
| Subjects: | |
| Online Access: | http://mss.academiaromana-is.ro/mem_sc_st_2019/2_Blair%20MSS%202019.pdf |
| _version_ | 1818851302203981824 |
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| author | David E. Blair |
| author_facet | David E. Blair |
| author_sort | David E. Blair |
| collection | DOAJ |
| description | In 2002, Frédéric Bourgeois [2] showed that, given a compact contact manifold M 2n–1, the product M 2n–1 × T 2 also carries a contact form; then, as a corollary he observed that all odd-dimensional tori have contact forms. The idea is to use an open book decomposition of M 2n–1 that is compatible with its contact structure [4] to produce contact forms on the product M 2n–1 × T 2. Here we first find the Reeb vector field and then a method for constructing associated metrics for contact forms of the type studied by Bourgeois. We will also discuss S 2 × T 2 in some detail. While the procedure would apply to tori, the construction is quite difficult and we will make only some remarks. |
| first_indexed | 2024-12-19T07:02:52Z |
| format | Article |
| id | doaj.art-ad450dd3f4ce4880a42f9aabbb39bca5 |
| institution | Directory Open Access Journal |
| issn | 1224-1407 2343-7049 |
| language | English |
| last_indexed | 2024-12-19T07:02:52Z |
| publishDate | 2019-11-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Memoirs of the Scientific Sections of the Romanian Academy |
| spelling | doaj.art-ad450dd3f4ce4880a42f9aabbb39bca52022-12-21T20:31:22ZengPublishing House of the Romanian AcademyMemoirs of the Scientific Sections of the Romanian Academy1224-14072343-70492019-11-01XLII920Associated Metrics for Bourgeois’ Contact FormsDavid E. Blair0Department of Mathematics Michigan State University East Lansing, U.S.A.In 2002, Frédéric Bourgeois [2] showed that, given a compact contact manifold M 2n–1, the product M 2n–1 × T 2 also carries a contact form; then, as a corollary he observed that all odd-dimensional tori have contact forms. The idea is to use an open book decomposition of M 2n–1 that is compatible with its contact structure [4] to produce contact forms on the product M 2n–1 × T 2. Here we first find the Reeb vector field and then a method for constructing associated metrics for contact forms of the type studied by Bourgeois. We will also discuss S 2 × T 2 in some detail. While the procedure would apply to tori, the construction is quite difficult and we will make only some remarks.http://mss.academiaromana-is.ro/mem_sc_st_2019/2_Blair%20MSS%202019.pdfmathematical modelingapplied mathematicsnicole oresme14th century |
| spellingShingle | David E. Blair Associated Metrics for Bourgeois’ Contact Forms Memoirs of the Scientific Sections of the Romanian Academy mathematical modeling applied mathematics nicole oresme 14th century |
| title | Associated Metrics for Bourgeois’ Contact Forms |
| title_full | Associated Metrics for Bourgeois’ Contact Forms |
| title_fullStr | Associated Metrics for Bourgeois’ Contact Forms |
| title_full_unstemmed | Associated Metrics for Bourgeois’ Contact Forms |
| title_short | Associated Metrics for Bourgeois’ Contact Forms |
| title_sort | associated metrics for bourgeois contact forms |
| topic | mathematical modeling applied mathematics nicole oresme 14th century |
| url | http://mss.academiaromana-is.ro/mem_sc_st_2019/2_Blair%20MSS%202019.pdf |
| work_keys_str_mv | AT davideblair associatedmetricsforbourgeoiscontactforms |