scholarly journals The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle

1989 ◽  
Vol 125 (2) ◽  
pp. 355-367 ◽  
Author(s):  
Jean-Michel Bismut ◽  
Eric Vasserot
Keyword(s):  
Line Bundle ◽  
Analytic Torsion ◽  
Positive Line Bundle ◽  
Positive Line

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.

scholarly journals ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS

2015 ◽  
Vol 16 (2) ◽  
pp. 223-349 ◽  
Author(s):  
Jean-Michel Bismut ◽  
Xiaonan Ma ◽  
Weiping Zhang
Keyword(s):  
Vector Bundle ◽  
Line Bundle ◽  
Differential Form ◽  
Toeplitz Operators ◽  
Vector Bundles ◽  
Direct Image ◽  
Analytic Torsion ◽  
Leading Term ◽  
Positive Line Bundle ◽  
Positive Line

We use Toeplitz operators to evaluate the leading term in the asymptotics of the analytic torsion forms associated with a family of flat vector bundles $F_{p}$. For $p\in \mathbf{N}$, the flat vector bundle $F_{p}$ is the direct image of $L^{p}$, where $L$ is a holomorphic positive line bundle on the fibres of a flat fibration by compact Kähler manifolds. The leading term of the analytic torsion forms is the integral along the fibre of a locally defined differential form.

scholarly journals SCALING ASYMPTOTICS FOR QUANTIZED HAMILTONIAN FLOWS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250102 ◽  
Author(s):  
ROBERTO PAOLETTI
Keyword(s):  
Line Bundle ◽  
Symplectic Manifold ◽  
Natural Generalization ◽  
Local Scaling ◽  
Hamiltonian Flows ◽  
Szegő Kernel ◽  
Szego Kernel ◽  
Positive Line Bundle ◽  
Positive Line ◽  
Compact Symplectic Manifold

In recent years, the near diagonal asymptotics of the equivariant components of the Szegö kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map.

scholarly journals Käahler identity on Levi flat manifolds and application to the embedding

2000 ◽  
Vol 158 ◽  
pp. 87-93 ◽  
Author(s):  
Takeo Ohsawa ◽  
Nessim Sibony
Keyword(s):  
Line Bundle ◽  
Finite Order ◽  
Flat Manifold ◽  
Positive Line Bundle ◽  
Flat Manifolds ◽  
Positive Line

AbstractIt is shown that any compact Levi flat manifold admitting a positive line bundle is embeddable into ℙn by a CR mapping with an arbitrarily high, though finite, order of regularity.

Complex submanifolds, connections and asymptotics

2010 ◽  
Vol 53 (2) ◽  
pp. 373-383
Author(s):  
Tatyana Foth
Keyword(s):  
Line Bundle ◽  
Complex Manifold ◽  
Compact Complex Manifold ◽  
Line Bundles ◽  
Natural Connection ◽  
Complex Submanifolds ◽  
Positive Line Bundle ◽  
Positive Line

AbstractLet L → X be a positive line bundle on a compact complex manifold X. For compact submanifolds Y, S of X and a holomorphic submersion Y → S with compact fibre, we study curvature of a natural connection on certain line bundles on S.

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