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 |
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| Online Access: | http://mss.academiaromana-is.ro/mem_sc_st_2019/2_Blair%20MSS%202019.pdf |
| Summary: | 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. |
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| ISSN: | 1224-1407 2343-7049 |