Abstract
Let (V, ω) be a simply connected symplectic manifold and let G be a group acting on V preserving the symplectic form. Let \( \mathfrak{g} \) be the Lie algebra of G which consists of all left-invariant vector fields on G. Then any v ∈ \( \mathfrak{g} \) induces a one-parameter subgroup {øt} of G. Since G acts on V, ø t induces a vector field X v on V. It is well known that there exists a map m, called moment map, m : V→ \( \mathfrak{g} \)*, satisfying
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m is G-equivariant with respect to the co-adjoint action on \( \mathfrak{g} \)*,
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for all v ∈ \( \mathfrak{g} \) and all u ∈ TV, ω( u, X v = dm (u)(v).
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© 2000 Springer Basel AG
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Tian, G. (2000). Scalar Curvature as a moment Map. In: Canonical Metrics in Kähler Geometry. Lectures in Mathematics. ETH Zürich. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8389-4_4
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DOI: https://doi.org/10.1007/978-3-0348-8389-4_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6194-5
Online ISBN: 978-3-0348-8389-4
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