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

Chin-Yu Hsiao; Rung-Tzung Huang

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arXiv · 1605.07507

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

Chin-Yu Hsiao·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 $X$. We introduce the Fourier components of the Ray-Singer analytic torsion on $X$ with respect to the $S^1$-action. We establish an asymptotic formula for the Fourier components of the analytic torsion with respect to the $S^1$-action. This generalizes the asymptotic formula of Bismut and Vasserot on the holomorphic Ray-Singer torsion associated with high powers of a positive line bundle to strongly pseudoconvex CR manifolds with a transversal CR $S^1$-action.

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BibTeX RIS

Chin-Yu Hsiao, Rung-Tzung Huang. 2016-05-24. The asymptotics of the analytic torsion on CR manifolds with $S^1$ action. https://arxiv.org/abs/1605.07507

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