A homogeneous-pair framework computes curvatures, geodesics, and metric completions of conformal transformations, with new applications to G2 moduli and the Ebin metric.
The geometry of K\"ahler cones
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abstract
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.
fields
math.DG 1years
2019 1verdicts
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Conformal transformations of the pseudo-Riemannian metric of a homogeneous pair
A homogeneous-pair framework computes curvatures, geodesics, and metric completions of conformal transformations, with new applications to G2 moduli and the Ebin metric.