Geometric and analytic problems for a real submanifold in Cn with CR singularities

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（6）
• 页码范围: 995-1004
• 页数: 10页
• 语种: 英文
• DOI: 10.1007/s11425-016-9002-6

摘要

In this survey article,we present some known results and also propose some open questions related to the analytic and geometric aspects of Bishop submanifolds in a complex space.We mainly focus on those problems that the author and his coauthors have recently worked on.The article also contains an example of a Bishop submanifold in C3 of real codimension two,which cannot be quadratically flattened at a CR singular point but is CR non-minimal at any CR point.This provides a counter-example to a question asked in a private communication by Zaistev (2013).