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- W2891370703 abstract "A Kahler manifold (M, g) is Einstein when there exists (lambda in mathbb {R}) such that ρ = λω, where ω is the Kahler form associated to g and ρ is its Ricci form. The constant λ is called the Einstein constant and it turns out that λ = s∕2n, where s is the scalar curvature of the metric g and n the complex dimension of M (as a general reference for this chapter see e.g. Tian (Canonical Metrics in Kahler Geometry. Notes taken by Meike Akveld. Lectures in Mathematics ETH Zurich. Birkhauser Verlag, Basel, 2000)). If (omega =frac {i}{2} sum _{j=1}^{n}g_{alpha bar {beta }} dz_{alpha }wedge dbar {z}_{bar {beta }}) is the local expression of ω on an open set U with local coordinates (z1, …, zn) centered at some point p then the Ricci form is the 2-form on M of type (1, 1) defined by" @default.
- W2891370703 created "2018-09-27" @default.
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- W2891370703 date "2018-01-01" @default.
- W2891370703 modified "2023-09-27" @default.
- W2891370703 title "Kähler–Einstein Manifolds" @default.
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- W2891370703 doi "https://doi.org/10.1007/978-3-319-99483-3_4" @default.
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