Reduction Theorems for Manifolds with Degenerate 2-Form

doi:10.5802/jolt.461

Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 563-581

Abstract

We consider a manifold with a 2-form and an action of a Lie group on the manifold which preserves the form. We define a momentum map and study its properties in this context. In particular we obtain a reduction theorem. Then we apply our reduction theorem to a certain generalization of the contact metric manifolds.

Zbl

DOI: 10.5802/jolt.461

Classification: 53D20, 53C15, 53C25
Keywords: Degenerate symplectic form, momentum map, symplectic reduction, K,C,S-structures, generalized contact metric structure

@misc{JOLT_2007_17_3_a6,
     title = {Reduction {Theorems} for {Manifolds} with {Degenerate} {2-Form}},
     journal = {Journal of Lie Theory},
     pages = {563--581},
     year = {2007},
     volume = {17},
     number = {3},
     doi = {10.5802/jolt.461},
     zbl = {1144.53042},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.461/}
}

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Reduction Theorems for Manifolds with Degenerate 2-Form. Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 563-581. doi: 10.5802/jolt.461

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