Q-prime curvature on CR manifolds

Q-prime curvature, which was introduced by J. Case and P. Yang, is a local invariant of pseudo-hermitian structure on CR manifolds that can be defined only when the Q-curvature vanishes identically. It is considered as a secondary invariant on CR manifolds and, in 3-dimensions, its integral agrees w...

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Bibliographic Details
Published in:Differential geometry and its applications 2014-03, Vol.33, p.213-245
Main Author: Hirachi, Kengo
Format: Article
Language:English
Subjects:
Boundaries
Construction
CR invariant differential operators
CR manifolds
Curvature
Differential geometry
Integrals
Invariants
Manifolds
Mathematical analysis
Pluriharmonic functions
Pseudo-Einstein structures
Q-curvature
Strictly pseudoconvex domains
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Summary:Q-prime curvature, which was introduced by J. Case and P. Yang, is a local invariant of pseudo-hermitian structure on CR manifolds that can be defined only when the Q-curvature vanishes identically. It is considered as a secondary invariant on CR manifolds and, in 3-dimensions, its integral agrees with the Burns–Epstein invariant, a Chern–Simons type invariant in CR geometry. We give an ambient metric construction of the Q-prime curvature and study its basic properties. In particular, we show that, for the boundary of a strictly pseudoconvex domain in a Stein manifold, the integral of the Q-prime curvature is a global CR invariant, which generalizes the Burns–Epstein invariant to higher dimensions.
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2013.10.013