Mathematical Sciences: Problems in Kahler and Quaternionic Kahler Geometry

这个建议属于卡勒几何的范畴。研究了圆的微分同态群的商空间的几何性质；研究复射影空间和四元数空间中的极小拉格朗日曲面；几何有限四元数和Cayley双曲流形的拓扑结构也将被研究。卡勒几何是研究带有卡勒度规的复杂流形。复流形是一个弯曲空间，局部看起来像一个复数空间；然后Kahler度规在流形上定义一个与其复杂结构相容的距离函数。应该提到的是，只有引入复杂的结构，才有可能进行许多困难的计算；卡勒结构使得从几何上解释这些计算成为可能。这是微分几何领域中一个非常活跃的领域，并应用于现代物理学的部分领域。

9626136 Corlette This proposal lies in the area of Kahler geometry. The geometry of a quotient space of the group of diffeomorphisms of the circle will be studied; minimal Lagrangian surfaces in complex projective and quaternionic spaces will be studied; the topology of geometrically finite quaternionic and Cayley hyperbolic manifolds will be also be investigated. Kahler geometry is the study of complex (sub-) manifolds equipped with a Kahler metric. A complex manifold is a curved space which looks locally like a complex number space; a Kahler metric then defines a distance function on the manifold compatible with its complex structure. It should be mentioned that many difficult calculations are possible only with the introduction of a complex strucure; a Kahler structure makes it possible to interpret these calculations geometrically. This is a very active area within the field of differential geometry with applications to parts of modern physics.