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Szegő Kernel Asymptotics on Complete Strictly Pseudoconvex CR Manifolds.
Chin-Yu Hsiao1, George Marinescu2,3, Huan Wang4
1Institute of Mathematics, Academia Sinica, Taipei, Taiwan.
Journal of Geometric Analysis
|August 24, 2022
Summary
Researchers derived a Bochner-Kodaira-Nakano formula and Szegő kernel expansions for CR manifolds. This work demonstrates that these manifolds are locally CR embeddable, advancing geometric analysis.
Area of Science:
- Differential Geometry
- Complex Analysis
- Geometric Analysis
Background:
- CR manifolds are central objects in differential geometry and complex analysis.
- Understanding their geometric properties is crucial for various mathematical fields.
Purpose of the Study:
- To establish a Bochner-Kodaira-Nakano formula on complete strictly pseudoconvex CR manifolds.
- To derive Szegő kernel expansions under transversal CR action.
- To investigate the local CR embeddability of such manifolds.
Main Methods:
- Utilizing techniques from geometric analysis.
- Applying Bochner-Kodaira-Nakano type identities.
- Developing Szegő kernel expansion methods.
Main Results:
- A novel Bochner-Kodaira-Nakano formula is proven.
- Szegő kernel expansions are established on specified CR manifolds.
- The local CR embeddability of these manifolds is demonstrated.
Conclusions:
- The established formulas and expansions provide new insights into the geometry of CR manifolds.
- The results confirm the local CR embeddability under the given conditions.
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