Integrating holomorphic sectional curvatures

Author:

Gunnar Þór Magnússon

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Algebraic Geometry (math.AG), Complex Variables (math.CV)

journal:

date:

2023-07-02 16:00:00

Abstract

We calculate the $L^2$-norm of the holomorphic sectional curvature of a K\"ahler metric by representation-theoretic means. This yields a new proof that the holomorphic sectional curvature determines the whole curvature tensor. We then investigate what the holomorphic sectional curvature of a Hermitian metric determines and calculate the $L^2$-norm of the holomorphic bisectional curvature.

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