$\mathcal{I}^\prime$-curvatures in higher dimensions and the Hirachi conjecture

DOI10.2969/JMSJ/87718771arXiv2003.08201WikidataQ113702801 ScholiaQ113702801MaRDI QIDQ6336963

Yuya Takeuchi, Jeffrey S. Case

Publication date: 18 March 2020

Abstract: We construct higher-dimensional analogues of the $mathcal{I}^{p}rime$-curvature of Case and Gover in all CR dimensions $ngeq2$. Our $mathcal{I}^{p}rime$-curvatures all transform by a first-order linear differential operator under a change of contact form and their total integrals are independent of the choice of pseudo-Einstein contact form on a closed CR manifold. We exhibit examples where these total integrals depend on the choice of general contact form, and thereby produce counterexamples to the Hirachi conjecture in all CR dimensions $ngeq2$.

Mathematics Subject Classification ID

CR structures, CR operators, and generalizations (32V05)

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