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

DOI10.1016/J.AIM.2023.109023arXiv2210.05855MaRDI QIDQ6413636

Yuya Takeuchi

Publication date: 11 October 2022

Abstract: The $Q$-prime curvature is a local pseudo-Einstein invariant 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.

Mathematics Subject Classification ID

CR structures, CR operators, and generalizations (32V05) Differential invariants (local theory), geometric objects (53A55)

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