我們知道在柯西-黎曼(CR)幾何中，柯西-黎曼偏尼茲算子(CR Paneitz)起著關鍵作用。透過這一算子的深入理解與應用，特別是它的非負性，我們可以簡化一些估計，從而得到一些重要的結果。在這個計畫裏，我們想知道有多少CR流形被賦與一個非負偏尼茲算子。此外，我們想將這個問題轉換成一個 CR嵌入問題，看看他們之間的相互關係有多少。我們最近的研究結果表明這種現象。 我們將從研究一些例子和一些特殊情況開始。重複研讀大量有關CR嵌入問題的文章，並嘗試找出偏尼茲算子如何進來的點。我們也想找到一個天然的方法去證明當 擬赫米特扭率是零時，偏尼茲算子是非負的。 “自然”的意思在這裡意味著它可以擴展到更一般的情況。最後，經由這些例子和特殊情況的研究，我們 想要建立一個一般的理論。 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.. 研究期間：10008 ~ 10107
