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

INT-9903302布莱尔美国-保加利亚合作研究奖是一个关于“几何的四流形和扭曲空间”博士之间的大卫E。密歇根州立大学的布莱尔、西北伊利诺伊大学的泰迪·德拉吉奇博士、凯斯西储大学的布伦丹·福尔曼博士以及保加利亚科学院数学与信息学研究所的约翰·托多罗夫·达维多夫、奥列格·克拉斯特夫·穆什卡洛夫、维斯蒂斯拉夫·德拉戈米罗夫·阿波斯托洛夫博士。该提案的目的是进一步发展PI和他最近的两个博士之间的研究合作。保加利亚研究所的学生和研究人员。 本文拟研究：（1）Kahler度量和几乎Kahler度量的扭数构造;（2）Reimannian对称和3-对称扭数空间;（3）具有调和几乎复结构的扭数空间;（4）扭数空间截面的极小性;（5）紧致 *-Einstein Hermitian曲面的分类;（6）紧致双Hermitian曲面的分类;（7）具有特殊Weyl张量的紧致Almost-Kahler 4-流形;（8）扭量空间上的复切触结构;（9）李群上的复切触结构;（10）切触流形上的曲率和共形Anosov流。这项数学研究实现了汇集美国和保加利亚领先专家的计划目标，在平等，互惠和互利的基础上，在强烈的共同利益和能力领域联合收割机互补努力和能力。

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.***