{"title":"协维流形的等接触嵌入","authors":"Dishant M. Pancholi, Suhas Pandit","doi":"10.4310/jsg.2022.v20.n2.a3","DOIUrl":null,"url":null,"abstract":"The purpose of this article is to study co-dimension $2$ iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold $(M^{2n-1}, \\xi_M)$ iso-contact embeds in a contact manifold $(N^{2n+1}, \\xi_N),$ provided $M$ contact embeds in $(N, \\xi_N)$ with a trivial normal bundle and the contact structure induced on $M$ via this embedding is homotopic as an almost-contact structure to $\\xi_M.$ We apply this result to first establish that a closed contact $3$--manifold having no $2$--torsion in its second integral cohomology iso-contact embeds in the standard contact $5$--sphere if and only if the first Chern class of the contact structure is zero. Finally, we discuss iso-contact embeddings of closed simply connected contact $5$--manifolds.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2018-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Iso-contact embeddings of manifolds in co-dimension $2$\",\"authors\":\"Dishant M. Pancholi, Suhas Pandit\",\"doi\":\"10.4310/jsg.2022.v20.n2.a3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this article is to study co-dimension $2$ iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold $(M^{2n-1}, \\\\xi_M)$ iso-contact embeds in a contact manifold $(N^{2n+1}, \\\\xi_N),$ provided $M$ contact embeds in $(N, \\\\xi_N)$ with a trivial normal bundle and the contact structure induced on $M$ via this embedding is homotopic as an almost-contact structure to $\\\\xi_M.$ We apply this result to first establish that a closed contact $3$--manifold having no $2$--torsion in its second integral cohomology iso-contact embeds in the standard contact $5$--sphere if and only if the first Chern class of the contact structure is zero. Finally, we discuss iso-contact embeddings of closed simply connected contact $5$--manifolds.\",\"PeriodicalId\":50029,\"journal\":{\"name\":\"Journal of Symplectic Geometry\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2018-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Symplectic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/jsg.2022.v20.n2.a3\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symplectic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jsg.2022.v20.n2.a3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Iso-contact embeddings of manifolds in co-dimension $2$
The purpose of this article is to study co-dimension $2$ iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold $(M^{2n-1}, \xi_M)$ iso-contact embeds in a contact manifold $(N^{2n+1}, \xi_N),$ provided $M$ contact embeds in $(N, \xi_N)$ with a trivial normal bundle and the contact structure induced on $M$ via this embedding is homotopic as an almost-contact structure to $\xi_M.$ We apply this result to first establish that a closed contact $3$--manifold having no $2$--torsion in its second integral cohomology iso-contact embeds in the standard contact $5$--sphere if and only if the first Chern class of the contact structure is zero. Finally, we discuss iso-contact embeddings of closed simply connected contact $5$--manifolds.
期刊介绍:
Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.