Variation of total Q-prime curvature on CR manifolds

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 curvature agrees with the renormalized volume of such domains with respect to the complete Einstein-Kähler metric. In the appendix, by Rod Gover and the first author, we study the property of CR invariant differential operator of order 2(n+3) on 2n+1 dimensional CR manifolds that appears in the second variational formula of the total Q-prime curvature.

32 pages; Final version, accepted for publication in Advances in Math

References in corpus (2)

• The Ambient Obstruction Tensor and Q-Curvature
• CR-Invariants and the Scattering Operator for Complex Manifolds with Boundary

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• Bounded strictly pseudoconvex domains in ${\mathbb{C}}^2$ with obstruction flat boundary
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