Towards the cosymplectic topology
In this article, the cosymplectic analogue of the symplectic flux homomorphism of a compact connected cosymplectic manifold (M,η,ω)\left(M,\eta ,\omega ) with ∂M=∅\partial M=\varnothing is studied. This is a continuous map with respect to the C0{C}^{0}-metric, whose kernel is connected by smooth ar...
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-07-01
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| Series: | Complex Manifolds |
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| Online Access: | https://doi.org/10.1515/coma-2022-0151 |
| _version_ | 1797773462624796672 |
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| author | Tchuiaga Stéphane |
| author_facet | Tchuiaga Stéphane |
| author_sort | Tchuiaga Stéphane |
| collection | DOAJ |
| description | In this article, the cosymplectic analogue of the symplectic flux homomorphism of a compact connected cosymplectic manifold (M,η,ω)\left(M,\eta ,\omega ) with ∂M=∅\partial M=\varnothing is studied. This is a continuous map with respect to the C0{C}^{0}-metric, whose kernel is connected by smooth arcs and coincides with the subgroup of all weakly Hamiltonian diffeomorphisms. We discuss the cosymplectic analogue of the Weinstein’s chart, and derive that the group Gη,ω(M){G}_{\eta ,\omega }\left(M) of all cosymplectic diffeomorphisms isotopic to the identity map is locally contractible. A study of an analogue of Polterovich’s regularization process for co-Hamiltonian isotopies follows. Finally, we study Moser’s stability theorems for locally conformal cosymplectic manifolds. |
| first_indexed | 2024-03-12T22:06:53Z |
| format | Article |
| id | doaj.art-3062c73d7cfa4cb2afd7a6d10a7d2e65 |
| institution | Directory Open Access Journal |
| issn | 2300-7443 |
| language | English |
| last_indexed | 2024-03-12T22:06:53Z |
| publishDate | 2023-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Complex Manifolds |
| spelling | doaj.art-3062c73d7cfa4cb2afd7a6d10a7d2e652023-07-24T11:18:33ZengDe GruyterComplex Manifolds2300-74432023-07-01101174222710.1515/coma-2022-0151Towards the cosymplectic topologyTchuiaga Stéphane0Department of Mathematics of the University of Buea, South West Region, CameroonIn this article, the cosymplectic analogue of the symplectic flux homomorphism of a compact connected cosymplectic manifold (M,η,ω)\left(M,\eta ,\omega ) with ∂M=∅\partial M=\varnothing is studied. This is a continuous map with respect to the C0{C}^{0}-metric, whose kernel is connected by smooth arcs and coincides with the subgroup of all weakly Hamiltonian diffeomorphisms. We discuss the cosymplectic analogue of the Weinstein’s chart, and derive that the group Gη,ω(M){G}_{\eta ,\omega }\left(M) of all cosymplectic diffeomorphisms isotopic to the identity map is locally contractible. A study of an analogue of Polterovich’s regularization process for co-Hamiltonian isotopies follows. Finally, we study Moser’s stability theorems for locally conformal cosymplectic manifolds.https://doi.org/10.1515/coma-2022-0151locally conformal cosymplectic manifoldsflux homomorphismthe weinstein chartdiffeomorphismsdifferential forms53c2453c1553d0557r17 |
| spellingShingle | Tchuiaga Stéphane Towards the cosymplectic topology Complex Manifolds locally conformal cosymplectic manifolds flux homomorphism the weinstein chart diffeomorphisms differential forms 53c24 53c15 53d05 57r17 |
| title | Towards the cosymplectic topology |
| title_full | Towards the cosymplectic topology |
| title_fullStr | Towards the cosymplectic topology |
| title_full_unstemmed | Towards the cosymplectic topology |
| title_short | Towards the cosymplectic topology |
| title_sort | towards the cosymplectic topology |
| topic | locally conformal cosymplectic manifolds flux homomorphism the weinstein chart diffeomorphisms differential forms 53c24 53c15 53d05 57r17 |
| url | https://doi.org/10.1515/coma-2022-0151 |
| work_keys_str_mv | AT tchuiagastephane towardsthecosymplectictopology |