English

Variation of total Q-prime curvature on CR manifolds

Differential Geometry 2016-11-22 v4 Complex Variables

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-K\"ahler 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.

Keywords

Cite

@article{arxiv.1510.03221,
  title  = {Variation of total Q-prime curvature on CR manifolds},
  author = {Kengo Hirachi and Taiji Marugame and Yoshihiko Matsumoto},
  journal= {arXiv preprint arXiv:1510.03221},
  year   = {2016}
}

Comments

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