Abstract
>Tom Branson introduced the concept of Q-curvature in conformal geometry, in connection with the study of conformal anomaly of determinants of conformally invariant differential operators. The definition can be generalized to CR manifolds via Fefferman’s conformal structure on a circle bundle over CR manifolds, see [2]. Using this correspondence, one can translate the properties of conformal Q-curvature to the CR analogue. However, there has been an important missing piece in this correspondence.
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References
J.S. Case, P.C. Yang, A Paneitz-type operator for CR pluriharmonic functions (2013). https://getinfo.de/en/search/id/BLSE%3ARN340441836/A-Paneitz-type-operator-for-CR-pluriharmonic-functions/
C. Fefferman, K. Hirachi, Ambient metric construction of Q-curvature in conformal and CR geometries. Math. Res. Lett. 10, 819–832 (2003)
K. Hirachi, Q-prime curvature on CR manifolds. Differ. Geom. Appl. 33(Suppl.), 213–245 (2014). arXiv:1302.0489
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Hirachi, K. (2015). Variation of the Total Q-Prime Curvature in CR Geometry. In: González, M., Yang, P., Gambino, N., Kock, J. (eds) Extended Abstracts Fall 2013. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21284-5_5
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DOI: https://doi.org/10.1007/978-3-319-21284-5_5
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