Mathematical Sciences: Twistor Theory with Applications to Restricted Holonomy Geometries and Other Problems in Differential Geometry

数学科学：扭量理论及其在受限完整几何和微分几何中其他问题中的应用

• 批准号: 9307398
• 负责人: Jon Pitts
• 金额: $ 2.51万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307398&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Twistor; Theory; Applications

The proposed research entails a study of manifolds with affine connections of restricted holonomy and the geometry of submanifolds of certain classes of Riemanian symmetric spaces. Particular attention in the latter case will be paid to surfaces in quaternionic-Kaehler manifolds where such surfaces can be studied by complex-analytic means relative to an associated complex manifold. This research also entails a study of deformations of Einstein metrics on 4-manifolds.

拟议的研究需要研究流形与 限制完整性的仿射联络和 某些类的黎曼对称空间的子流形。 在后一种情况下，将特别注意表面 在四元数Kaehler流形中，这样的曲面可以 通过复分析方法研究相对于相关的 复流形 这项研究还需要研究 四维流形上的爱因斯坦度量的变形