Mathematical Sciences: Algebraic Geometry, Kahler Geometry

主要研究人员将研究twistor空间的代数结构、Kahler爱因斯坦度量的构造以及Kahler约化的应用。所采用的方法是微分几何和代数技术的结合。扭曲空间是与自对偶黎曼四维流形相联系的复三维空间。首席研究员将研究与复射影平面的连通和相关的扭曲空间。首席研究员还将研究在允许一个参数对称群的空间上的Kahler Einstein度量的构造。广义相对论建立在曲率与应力成正比的空间中。这些空间被称为爱因斯坦流形，出现在数学的许多分支中，知道给定空间何时具有爱因斯坦空间的结构是有用的。首席研究员将研究这个问题以及数学物理中出现的其他空间的结构。

The principal investigator will study the algebraic structure of twistor spaces, the construction of Kahler Einstein metrics and application of Kahler reduction. The methods to be employed are a combination of differential geometry and algebraic techniques. A twistor space is a complex three dimensional space associated to a self-dual Riemannian four dimensional manifold. The principal investigator will study those twistor spaces associated with the connected sums of complex projective planes. The principal investigator will also study the construction of Kahler Einstein metrics on spaces admitting a one parameter group of symmetries. The general theory of relativity is set in spaces in which curvature is proportional to stress. These spaces, called Einstein manifolds, arise in many branches of mathematics and it is useful to know when a given space has the structure of an Einstein space. The principal investigator will study this question as well as the structure of other spaces which arise in mathematical physics.