Riemannian Manifolds of Positive Curvature
Riemannian Manifolds of Positive Curvature
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DOI：
10.11429/emath1996.2007.autumn-meeting1_14
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发表时间：
2011-06
期刊：
影响因子：
--
通讯作者：
R. Schoen
中科院分区：
文献类型：
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作者：
R. Schoen
正截面曲率的研究是黎曼几何中最古老的追求之一，但尽管许多研究人员付出了相当大的努力，基本问题仍然没有答案。在本讲座中，我们将简要总结这一领域的知识状况，并概述已取得成功的技术。这些技术包括测地线和比较方法，最小曲面方法和Ricci流。然后我们将描述我们最近的工作（见[18]，[21]，[22]），它使用里奇流来解决可微球定理;也就是说，截面曲率为1/4-pinching的流形的完整分类。
The study of positive sectional curvature is one of the oldest pursuits in Riemannian geometry, but despite the considerable efforts of many researchers, basic questions remain unanswered. In this lecture we will briefly summarize the state of knowledge in this area and outline the techniques which have had success. These techniques include geodesic and comparison methods, minimal surface methods, and Ricci flow. We will then describe our recent work (see [18], [21], [22]) which uses the Ricci flow to resolve the differentiable sphere theorem; that is, the complete classification of manifolds whose sectional curvatures are 1/4-pinched.