### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 010, 8 pages      arXiv:1711.01724      https://doi.org/10.3842/SIGMA.2018.010

### Some Remarks on the Total CR $Q$ and $Q^\prime$-Curvatures

Taiji Marugame
Institute of Mathematics, Academia Sinica, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan

Received November 09, 2017, in final form February 12, 2018; Published online February 14, 2018

Abstract
We prove that the total CR $Q$-curvature vanishes for any compact strictly pseudoconvex CR manifold. We also prove the formal self-adjointness of the $P^\prime$-operator and the CR invariance of the total $Q^\prime$-curvature for any pseudo-Einstein manifold without the assumption that it bounds a Stein manifold.

Key words: CR manifolds; $Q$-curvature; $P^\prime$-operator; $Q^\prime$-curvature.

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