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arXiv · 2210.05855

Generalizations of the $Q$-prime curvature via renormalized characteristic forms

Yuya Takeuchi
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Abstract

The $Q$-prime curvature is a local pseudo-Einstein invariant on CR manifolds defined by Case and Yang, and Hirachi. Its integral, the total $Q$-prime curvature, gives a non-trivial global CR invariant. On the other hand, Marugame has constructed a family of global CR invariants via renormalized characteristic forms, which contains the total $Q$-prime curvature. In this paper, we introduce a generalization of the $Q$-prime curvature for each renormalized characteristic form, and show that its integral coincides with Marugame's CR invariant. We also study generalizations of the critical CR GJMS operator and the $P$-prime operator, which are related to the transformation laws of our new curvatures under conformal change.

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Yuya Takeuchi. 2022-10-12. Generalizations of the $Q$-prime curvature via renormalized characteristic forms. https://doi.org/10.1016/j.aim.2023.109023

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