Mathematical Sciences: Algebraic Geometry, Kahler Geometry

首席研究员将研究代数结构 扭量空间，Kahler Einstein度规的构建， Kahler还原法的应用所采用的方法是 微分几何和代数技术的结合。一 扭量空间是一个复杂的三维空间， 自对偶黎曼四维流形校长 研究人员将研究那些与 复射影平面的连通和校长 研究人员还将研究卡勒·爱因斯坦的结构 度量空间允许一个参数组的对称性。 广义相对论是建立在这样的空间中的， 曲率与应力成正比。这些空间，被称为爱因斯坦 流形，出现在数学的许多分支，它是有用的， 知道一个给定的空间何时具有爱因斯坦空间的结构。 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.