Mathematical Sciences: Geometric Approach to Weinstein Conjecture

数学科学：韦恩斯坦猜想的几何方法

• 批准号: 9001861
• 负责人: Augustin Banyaga
• 金额: $ 4.77万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001861&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Approach; Weinstein

The principal investigator will study the existence of compact leaves in contact foliations of compact contact manifolds. The existence of these foliations was conjectured by Weinstein. Several special cases have been solved by this investigator and by other mathematicians. Lickorish surgical techniques will be used to investigate the three-dimensional version of the problem. Okumura's theory will be applied to the problem in the case of hypersurfaces with contact types in Kaehler manifolds. Diffeomorphism groups will also be studied. "Manifolds" are generalized surfaces. These may be filled with collections of lower dimensional "leaves." Such collections of leaves are called "foliations." The principal investigator will study leaves which do not wrap on continuously but actually close up. These are called in the literature, "compact leaves." Such are particularly important in applications to other sciences in that they represent, in a general sense, behavior which repeats indefinitely.

首席研究员将研究紧凑接触流形的接触叶中是否存在紧凑叶。 韦恩斯坦推测这些叶子的存在。 这位研究者和其他数学家已经解决了一些特殊情况。 Lickorish 外科技术将用于研究该问题的三维版本。 奥村的理论将应用于具有凯勒流形接触类型的超曲面情况下的问题。 微分同胚群也将被研究。 “流形”是广义的表面。 这些可能充满了低维“叶子”的集合。 这种叶子的集合称为“叶状结构”。 首席研究员将研究那些不是连续缠绕而是实际上闭合的叶子。 这些在文献中被称为“紧凑叶”。 这在其他科学的应用中尤其重要，因为它们在一般意义上代表无限重复的行为。