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arXiv · 1706.01078

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

Rung-Tzung Huang
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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.

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Rung-Tzung Huang. 2017-06-04. The anomaly formula of the analytic torsion on CR manifolds with $S^1$ action. https://arxiv.org/abs/1706.01078

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