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The Anomaly Formula of the Analytic Torsion on CR Manifolds with S^1 action
by Rung-Tzung Huang

Vol. 12 No. 2 (2017) P.153~P.203
 DOI: https://doi.org/10.21915/BIMAS.2017204 10.21915/BIMAS.2017204

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.

KEYWORDS
determinant, Ray-Singer torsion, CR manifolds.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: Primary: 58J52, 58J28; Secondary: 57Q10.

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