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

Jeffrey S. Case; Yuya Takeuchi

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arXiv · 2003.08201

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

Jeffrey S. Case·Yuya Takeuchi

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Abstract

We construct higher-dimensional analogues of the $\mathcal{I}^\prime$-curvature of Case and Gover in all CR dimensions $n\geq2$. 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 $n\geq2$.

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Jeffrey S. Case, Yuya Takeuchi. 2020-03-18. $\mathcal{I}^\prime$-curvatures in higher dimensions and the Hirachi conjecture. https://arxiv.org/abs/2003.08201

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