Mathematical Sciences: Geometry of Submanifolds

首席研究员将研究 R^n中具有简单局部不变量的子流形，紧嵌入 在Lie球面变换下， 的等距浸入的双曲n-空间到奇- 维欧氏空间 子流形是数学家对曲面的推广 它们位于普通的三维空间中。 两个例子- 维子流形是球体，内管的表皮， 和无限长的圆柱体。 三度空间 是爱因斯坦四维空间的子流形 时空 首席研究员将深入研究几个 这些子流形位于它们的 周围空间。

The principal investigator will study the geometry of submanifolds of R^n with simple local invariants, taut embeddings under Lie sphere transformations, and the geometry of the space of isometric immersions of hyperbolic n-space into odd- dimensional Euclidean space. Submanifolds are mathematician's generalizations of surfaces which lie in ordinary three-dimensional space. Examples of two- dimensional submanifolds are spheres, the skin of an inner tube, and infinitely-long cylinders. The three-dimensional space in which we live is a submanifold of Einstein's four-dimensional space-time. The principal investigator will study several deep problems which concern the way these submanifolds lie in their ambient spaces.