The anomaly formula of the analytic torsion on CR manifolds with $S^1$ action

Abstract

Let $X$ be a compact connected strongly pseudoconvex CR manifold of dimension $2n+1,n\ge 1$ with a transversal CR $S^1$-action on $X$. In this paper we introduce the Quillen metric on the determinant line of the Fourier components of the Kohn-Rossi cohomology on $X$ with respect to the $S^1$-action. We study the behavior of the Quillen metric under the change of the metrics on the manifold $X$ and on the vector bundle over $X$. We obtain an anomaly formula for the Quillen metric on $X$ with respect to the $S^1$-action.

36 pages

References in corpus (3)

• On the full asymptotic of analytic torsion
• On the stability of equivariant embedding of compact CR manifolds with circle action
• The asymptotics of the analytic torsion on CR manifolds with $S^1$ action