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Integrating holomorphic sectional curvatures

Differential Geometry 2023-07-06 v1 Algebraic Geometry Complex Variables

Abstract

We calculate the L2L^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 L2L^2-norm of the holomorphic bisectional curvature.

Keywords

Cite

@article{arxiv.2307.01332,
  title  = {Integrating holomorphic sectional curvatures},
  author = {Gunnar Þór Magnússon},
  journal= {arXiv preprint arXiv:2307.01332},
  year   = {2023}
}

Comments

9 pages, comments welcome

R2 v1 2026-06-28T11:21:13.719Z