Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds

本研究项目旨在系统地研究柯西-黎曼流形及其全纯映射和自同构，其方法是基于 陈-莫泽型范式。柯西-黎曼流形的重要性源于它们将复数结构和全纯与实流形的黎曼性质联系起来。构造高维Levi-非退化CR-流形的Chern-Moser标准形的模拟以及它们之间的CR-映射的推广是复分析的主要目标。识别Chern-Moser链和等变线性化各向同性自同构是几何学的主要目标。

This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form for multicodimensional Levi-nondegenerate CR-manifolds and extension of CR-mappings between them are major goals in complex analysis. Identification of Chern-Moser chains and equivariant linearisation of isotropy automorphisms are major goals in geometry.