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研究生： 陳雋介
Chun-Chien Chen
論文名稱： Product Formula for Analytic Torsion on CR manifolds with S^1-action
指導教授： 黃榮宗
Rung-Tzung Huang
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2024
畢業學年度： 112
語文別： 英文
論文頁數： 29
中文關鍵詞： 柯西黎曼流形 、分析橈率 、全純橈率
外文關鍵詞： analytic torsion, CR manifold, holomorphic torsion
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    • 在這篇論文中，我們先回顧Ray 和Singer 所引進的全純撓率的定義和一些性質，包括了乘積公式。接著，我們回顧了黃榮宗老師和蕭欽玉老師所引進的在有S^1-action 的柯西黎曼流形上解析橈率的傅立葉分量的定義。最後，我們得到了一些在有S^1-action 的柯西黎曼流形上解析橈率的性質，包括了乘積公式。

    In this thesis we first recall the definition and some properties, including product formula, of holomorphic torsion of Ray and Singer. Then we recall the definition of the Fourier components of the analytic torsion on CR manifolds with S^1-action of Huang and Hsiao. Finally, we obtain some properties, including product formula, of the Fourier components of the analytic torsion on CR manifolds with S^1-action.

    摘要 i Abstract ii 1. Introduction 1 2. Product formula for Holomorphic Torsion 2 2.1. The ∂ operator 2 2.2. The Kodaira Laplacian 4 2.3. Mellin transformation 5 2.4. Analytic Torsion on Complex Manifold 6 3. Product formula for CR Manifolds with S1action 11 3.1. CR manifolds 11 3.2. ∂b-complex 12 3.3. The Kohn Laplacian 13 3.4. CR manifolds with circle action 15 3.5. Heat Kernels of The Kohn Laplacians 17 3.6. Fourier Component of The Analytic Torsion 18 3.7. Analytic Torsion on CR manifolds with S^1 Action 20 Bibliography 23

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