Renormalized characteristic forms of the Cheng--Yau metric and global CR invariants

Taiji Marugame

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arXiv · 1912.10684

Renormalized characteristic forms of the Cheng--Yau metric and global CR invariants

Taiji Marugame

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Abstract

For each invariant polynomial $\Phi$, we construct a global CR invariant via the renormalized characteristic form of the Cheng--Yau metric on a strictly pseudoconvex domain. When the degree of $\Phi$ is 0, the invariant agrees with the total $Q'$-curvature. When the degree is equal to the CR dimension, we construct a primed pseudo-hermitian invariant $\mathcal{I}'_\Phi$ which integrates to the corresponding CR invariant. These are generalizations of the $\mathcal{I}'$-curvature on CR five-manifolds, introduced by Case--Gover.

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Taiji Marugame. 2019-12-23. Renormalized characteristic forms of the Cheng--Yau metric and global CR invariants. https://arxiv.org/abs/1912.10684

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