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

柯西-黎曼流形研究中的范式和Chern-Moser联系

• 批准号: DP0450725
• 负责人: A/Prof Vladimir Ejov
• 金额: $ 11.49万
• 依托单位: University of South Australia
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2004
• 资助国家: 澳大利亚
• 起止时间: 2004-01-01 至 2006-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0450725
• 关键词: Normal; forms; Chern; Moser; connection

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.

该研究项目旨在系统地研究柯西-黎曼流形、它们的全纯映射和自同构，通过基于 Chern-Moser 型范式。柯西-黎曼流形的重要性源于以下事实：它们将复杂结构和全纯性与实流形的黎曼性质联系起来。构建多维 Levi 非简并 CR 流形的 Chern-Moser 范式的类似物以及它们之间 CR 映射的扩展是复分析的主要目标。陈-莫泽链的识别和各向同性自同构的等变线性化是几何学的主要目标。