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The geometry of K\"ahler cones

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arxiv 1211.6934 v1 pith:LABY25RT submitted 2012-11-29 math.AG math.CVmath.DG

Gunnar THór Magnússon This is my paper · ORCID
classification math.AGmath.CVmath.DG
keywords ahlerconemetricmanifoldcarriescohomologycompactcompleteness
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The K\"ahler cone of a compact manifold carries a natural Riemannian metric, given by the intersection product of its cohomology ring. We write down the curvature tensor of this metric by embedding the K\"ahler cone in the space of hermitian metrics on the underlying manifold. After discussing weak functorality and completeness properties, we give a relative version of both the K\"ahler cone and the metric.

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  1. Conformal transformations of the pseudo-Riemannian metric of a homogeneous pair

    math.DG 2019-08 conditional novelty 7.0 of 10

    A homogeneous-pair framework computes curvatures, geodesics, and metric completions of conformal transformations, with new applications to G2 moduli and the Ebin metric.

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