Godbillon-Vey type functional for almost contact manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912130817589248 |
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| author | Rovenski, Vladimir |
| author_facet | Rovenski, Vladimir |
| contents | Many contact metric manifolds are critical points of curvature functionals restricted to spaces of associated metrics. The Godbillon-Vey functional has never been considered in a variational context in contact geometry. Recently we extended this functional from foliations to arbitrary plane fields on a 3-dimensional manifold, so, the following question arises: can one use the Godbillon-Vey functional to find optimal almost contact manifolds? In the paper, we introduce a Godbillon-Vey type functional for a 3-dimensional almost contact manifold and find its Euler-Lagrange equations for all variations preserving the Reeb vector field. We construct critical (for our functional) 3-dimensional almost contact manifolds having a double-twisted product structure, these solutions belong to the class $C_{5}\oplus C_{12}$ according to Chinea-Gonzalez classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Godbillon-Vey type functional for almost contact manifolds Rovenski, Vladimir Differential Geometry Many contact metric manifolds are critical points of curvature functionals restricted to spaces of associated metrics. The Godbillon-Vey functional has never been considered in a variational context in contact geometry. Recently we extended this functional from foliations to arbitrary plane fields on a 3-dimensional manifold, so, the following question arises: can one use the Godbillon-Vey functional to find optimal almost contact manifolds? In the paper, we introduce a Godbillon-Vey type functional for a 3-dimensional almost contact manifold and find its Euler-Lagrange equations for all variations preserving the Reeb vector field. We construct critical (for our functional) 3-dimensional almost contact manifolds having a double-twisted product structure, these solutions belong to the class $C_{5}\oplus C_{12}$ according to Chinea-Gonzalez classification. |
| title | Godbillon-Vey type functional for almost contact manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.11857 |