scholarly journals The Asymptotics of the $L^2$-analytic Torsion on CR Manifolds with $S^1$ Action

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Rung-Tzung Huang ◽  
Guokuan Shao
Keyword(s):  
Analytic Torsion ◽  
Cr Manifolds

scholarly journals The asymptotics of the analytic torsion on CR manifolds with S1 action

2019 ◽  
Vol 21 (04) ◽  
pp. 1750094 ◽  
Author(s):  
Chin-Yu Hsiao ◽  
Rung-Tzung Huang
Keyword(s):  
Line Bundle ◽  
Asymptotic Formula ◽  
Analytic Torsion ◽  
Cr Manifold ◽  
Cr Manifolds ◽  
Dimension Formula ◽  
Positive Line Bundle ◽  
Positive Line

Let [Formula: see text] be a compact connected strongly pseudoconvex CR manifold of dimension [Formula: see text], [Formula: see text] with a transversal CR [Formula: see text]-action on [Formula: see text]. We introduce the Fourier components of the Ray–Singer analytic torsion on [Formula: see text] with respect to the [Formula: see text]-action. We establish an asymptotic formula for the Fourier components of the analytic torsion with respect to the [Formula: see text]-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 [Formula: see text]-action.

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