U.S.-Bulgarian Cooperative Research: "Geometry of Four-Manifolds and Twistor Spaces"

美国-保加利亚合作研究：“四流形和扭曲空间的几何”

• 批准号: 9903302
• 负责人: David Blair
• 金额: $ 2.88万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-05-01 至 2003-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9903302&HistoricalAwards=false
• 关键词: U.S.; Bulgarian; Cooperative; Research; Geometry

INT-9903302BlairThis U.S.-Bulgaria Cooperative Research award is for a project on "Geometry of four-manifolds and twister spaces" between Dr. David E. Blair of Michigan State University, Dr. Tedi Draghici of Northwestern Illinois University, Dr. Brendan Foreman of Case Western Reserve University, and Drs. Johann Todorov Davidov, Oleg Krastev Mushkarov, Vestislav Dragomirov Apostolov of the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences. The objective of this proposal is to further develop research collaborations between the PI and two of his recent Ph.D. students and researchers from the Bulgarian Institute. The researchers propose to study: (1) Twistorial construction of Kahler and almost Kahler metrics; (2) Reimannian symmetric and 3-symmetric twistor spaces; (3) Twistor spaces with harmonic almost-complex structures; (4) Minimality of sections of twistor spaces; (5) Classification of compact *-Einstein Hermitian surfaces; (6) Classification of compact bi-Hermitian surfaces; (7) Compact almost-Kahler 4-manifolds with special Weyl tensor; (8) Complex contact structures on twistor spaces; (9) Complex contact structures on Lie groups; (10) Curvature and conformally Anosov flows on contact manifolds. This research in mathematics fulfills the program objectives of bringing together leading experts in the U.S. and Bulgaria to combine complementary efforts and capabilities in areas of strong mutual interest and competence on the basis of equality, reciprocity, and mutuality of benefit.***

这个美国-保加利亚合作研究奖是为密歇根州立大学的David E. Blair博士、伊利诺斯西北大学的Tedi Draghici博士、凯斯西储大学的Brendan Foreman博士和美国国家科学委员会的Brendan Foreman博士共同研究的“四流形和扭曲空间的几何”项目颁发的。保加利亚科学院数学与信息研究所的Johann Todorov Davidov， Oleg Krastev Mushkarov, Vestislav Dragomirov Apostolov。这项建议的目的是进一步发展PI与他最近的两名博士生和保加利亚研究所的研究人员之间的研究合作。研究者建议研究：(1)Kahler和几乎Kahler度量的扭曲构造；(2)黎曼对称和3对称扭转空间；(3)具有谐波几乎复杂结构的扭转空间；(4)扭转空间截面的极小性；(5)紧*-爱因斯坦厄米曲面的分类；(6)紧致双厄密曲面的分类；(7)具有特殊Weyl张量的紧致几乎kahler 4流形；(8)扭转空间上复杂的接触结构；(9)李群上的复杂接触结构；（10）接触流形上的曲率和共形Anosov流。这项数学研究实现了将美国和保加利亚的顶尖专家聚集在一起的项目目标，在平等、互惠和互利的基础上，在共同感兴趣和能力强的领域结合互补的努力和能力