三維柯西-黎曼流形偏尼茲算子與嵌入性;The Paneitz Operator and Embeddability for 3d Cauchy-Riemann Manifolds

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/63140

Title:	三維柯西-黎曼流形偏尼茲算子與嵌入性;The Paneitz Operator and Embeddability for 3d Cauchy-Riemann Manifolds
Authors:	邱鴻麟
Contributors:	國立中央大學數學系
Keywords:	數學;物理
Date:	2012-12-01
Issue Date:	2014-03-17 14:19:59 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	研究期間：10108~10207;The CR Paneitz operator plays a key role in CR geometry. By means of properties of this operator,e.g.its nonnegativity, we can simplify some estimates and thus get some important results.In this project, we would like to know how many CR manifolds are associated with a nonnegative Paneitz operator.In addition, we would like to convert this problem into a CR embedding problem and see how much they relate to each other. Our recent work reveals such a phenomenon. We will start with studing some examples and some special case. To review a lot of articles about the subject of embedding problem and try to find out how the Paneitz operator come in. We also want to find a natural method to prove the nonnegativity of the Paneitz operator when the pseudohermitian torsion is free. The “natural” here means that it can be extended to show this in a more general case. Finally, we would like to build a general theory by means of this studing of examples and special cases..
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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