Corpus ID: 118778793

# Q and Q-prime curvature in CR geometry

@article{Hirachi2014QAQ,
title={Q and Q-prime curvature in CR geometry},
author={K. Hirachi},
journal={arXiv: Differential Geometry},
year={2014}
}
• K. Hirachi
• Published 9 May 2014
• Mathematics
• arXiv: Differential Geometry
The Q-curvature has been playing a central role in conformal geometry since its discovery by T. Branson. It has natural analogy in CR geometry, however, the CR Q-curvature vanishes on the boundary of a strictly pseudoconvex domain in C^{n+1} with a natural choice of contact form. This fact enables us to define a "secondary" Q-curvature, which we call Q-prime curvature (it was first introduced by J. Case and P. Yang in the case n=1). The integral of the Q-prime curvature, the total Q-prime… Expand
2 Citations
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Abstract We derive variational formulas for the total Q -prime curvature under the deformation of strictly pseudoconvex domains in a complex manifold. We also show that the total Q -prime curvatureExpand

#### References

SHOWING 1-10 OF 27 REFERENCES
Q-prime curvature on CR manifolds
Abstract 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 vanishesExpand
A global invariant for three dimensional CR-manifolds
• Mathematics
• 1988
In this note we define a global, R-valued invariant of a compact, strictly pseudoconvex 3-dimensional CR-manifold M whose holomorphic tangent bundle is trivial. The invariant arises as the evaluationExpand
GJMS operators, Q-curvature, and obstruction tensor of partially integrable CR manifolds
We extend the notions of CR GJMS operators and Q-curvature to the case of partially integrable CR structures. The total integral of the CR Q-curvature turns out to be a global invariant of compactExpand
$Q$-Curvature and Poincaré Metrics
• Mathematics
• 2001
This article presents a new definition of Branson's Q-curvature in even-dimensional conformal geometry. We derive the Q-curvature as a coefficient in the asymptotic expansion of the formal solutionExpand
Ambient metric construction of Q-curvature in conformal and CR geometries
• Mathematics
• 2003
We give a geometric derivation of Branson's Q-curvature in terms of the ambient metric associated with conformal structures; it naturally follows from the ambient metric construction of conformallyExpand
Characteristic numbers of bounded domains
• Mathematics
• 1990
A fundamental problem in several complex variables is to find computable invariants of complex manifolds with strictly pseudoconvex boundaries. The foci of this subject have been: the construction ofExpand
The Ambient Obstruction Tensor and Q-Curvature
• Mathematics
• 2004
|W |, where W denotes the Weyl tensor. A generalization of the Bach tensor to higher even dimensional manifolds was indicated in [FG1]. This “ambient obstruction tensor”, which, suitably normalized,Expand
Logarithmic singularity of the Szego kernel and a global invariant of strictly pseudoconvex domains
This paper is a continuation of Fefferman's program [7] for studying the geometry and analysis of strictly pseudoconvex domains. The key idea of the program is to consider the Bergman and Szeg?Expand
INVARIANT THEORY OF THE BERGMAN KERNEL OF STRICTLY PSEUDOCONVEX DOMAINS
In the paper “Parabolic invariant theory in complex analysis [16],” Fefferman proposed a program of studying the geometry and analysis of strictly pseudoconvex domains (with C∞ boundary). His basicExpand
Complex Geometry, Lect. Notes in Pure and Appl. Math. 143, 67-76, Dekker, 1993 SCALAR PSEUDO-HERMITIAN INVARIANTS AND THE SZEGÖ KERNEL ON THREE-DIMENSIONAL CR MANIFOLDS
Let M be a three-dimensional strictly pseudoconvex CR manifold which bounds a relatively compact domain in C. We fix a Levi metric on M , which is called a pseudohermitian structure, and define theExpand