A locally conformally symplectic (LCS) form is an almost symplectic form ω such that a closed one-form θ exists with dω = θ ∧ ω. A fiber bundle with LCS fiber (F, ω, θ) is called LCS if the transition maps are diffeomorphisms of F preserving ω (and hence θ). In this paper, we find conditions for the total space of an LCS fiber bundle to admit an LCS form which restricts to the LCS form of the fibers. This is done by using the coupling form introduced by Sternberg and Weinstein, [GLS], in the symplectic case. The construction is related to an adapted Hamiltonian action called twisted Hamiltonian which we study in detail. Moreover, we give examples of such actions and discuss compatibility properties with respect to LCS reduction of LCS fiber bundles. We end with a glimpse towards the locally conformally Kähler case.
Otiman, A. (2018). Locally conformally symplectic bundles. JOURNAL OF SYMPLECTIC GEOMETRY, 16(5), 1377-1408 [10.4310/jsg.2018.v16.n5.a5].
Locally conformally symplectic bundles
Otiman A.
2018-01-01
Abstract
A locally conformally symplectic (LCS) form is an almost symplectic form ω such that a closed one-form θ exists with dω = θ ∧ ω. A fiber bundle with LCS fiber (F, ω, θ) is called LCS if the transition maps are diffeomorphisms of F preserving ω (and hence θ). In this paper, we find conditions for the total space of an LCS fiber bundle to admit an LCS form which restricts to the LCS form of the fibers. This is done by using the coupling form introduced by Sternberg and Weinstein, [GLS], in the symplectic case. The construction is related to an adapted Hamiltonian action called twisted Hamiltonian which we study in detail. Moreover, we give examples of such actions and discuss compatibility properties with respect to LCS reduction of LCS fiber bundles. We end with a glimpse towards the locally conformally Kähler case.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.