Hofer-Like Geometry and Flux Theory. Issue 2 (3rd July 2021)
- Record Type:
- Journal Article
- Title:
- Hofer-Like Geometry and Flux Theory. Issue 2 (3rd July 2021)
- Main Title:
- Hofer-Like Geometry and Flux Theory
- Authors:
- Tchuiaga, Stéphane
- Abstract:
- Abstract: This paper meticulously revisit and study the flux geometry of any compact connected oriented manifold ( M, Ω). We generalize several well- known factorization results, exhibit some orbital conditions under which flux geometry can be studied, give a proof of the discreteness of the flux group for volume-preserving diffeomorphisms, derive that any smooth isotopy in the group of all vanishing-flux volume-preserving diffeomorphisms is a vanishing- flux path, and show that the kernel of flux for volume-preserving diffeomorphisms is C 1 −closed inside the group of all volume-preserving diffeomorphisms isotopic to the identity map: We recover several well-known results from symplectic geometry. We use the above studies to construct a right-invariant metric on the group of all volume-preserving diffeomorphisms isotopic to the identity map and study the induced geometry. In the case of a symplectic volume form, the restriction of our metric to the group Ham ( N, ω ), of all Hamiltonian diffeomorphisms of a closed symplectic manifold ( N, ω ), is controlled from above by the usual Hofer metric in general, while the Hofer-like metric control our metric in the case where the Riemannian structure is compatible with the symplectic structure (in particular, our construction implies the non-degeneracy of the Hofer and Hofer-like norms).
- Is Part Of:
- Journal of dynamical systems and geometric theories. Volume 19:Issue 2(2021)
- Journal:
- Journal of dynamical systems and geometric theories
- Issue:
- Volume 19:Issue 2(2021)
- Issue Display:
- Volume 19, Issue 2 (2021)
- Year:
- 2021
- Volume:
- 19
- Issue:
- 2
- Issue Sort Value:
- 2021-0019-0002-0000
- Page Start:
- 227
- Page End:
- 270
- Publication Date:
- 2021-07-03
- Subjects:
- 53C24 -- 53D05 -- 57R50
Rigidity -- Symplectic manifolds -- Differential topological aspects of volume-preserving diffeomorphisms -- Isotopies -- Homotopy -- Metrics
Differentiable dynamical systems -- Periodicals
Geometry -- Periodicals
Differentiable dynamical systems
Geometry
Periodicals
515.39 - Journal URLs:
- http://www.connectjournals.com/jdsgt ↗
http://www.tandfonline.com/loi/tdsg20 ↗
http://www.tarupublications.com/journals/jdsgt/scope-of%20the-journal.htm ↗ - DOI:
- 10.1080/1726037X.2021.2011110 ↗
- Languages:
- English
- ISSNs:
- 1726-037X
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD Digital store
- Ingest File:
- 20434.xml