Abstract
We construct higher-dimensional analogues of the $\mathcal{I}^{\prime}$-curvature of Case and Gover in all CR dimensions $n \geq 2$. Our $\mathcal{I}^{\prime}$-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 $n \geq 2$.
Funding Statement
The first author was supported by a grant from the Simons Foundation (Grant No. 524601). The second author was supported by JSPS Research Fellowship for Young Scientists and JSPS KAKENHI Grant Numbers JP19J00063 and JP21K13792.
Citation
Jeffrey S. CASE. Yuya TAKEUCHI. "$\mathcal{I}^{\prime}$-curvatures in higher dimensions and the Hirachi conjecture." J. Math. Soc. Japan 75 (1) 291 - 328, January, 2023. https://doi.org/10.2969/jmsj/87718771
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