Canonical structure of manifolds and their application in the geometric topology View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2009-2012

FUNDING AMOUNT

1350000 CNY

ABSTRACT

The project belongs to the modern application of differential geometry in the field of geometric analysis, which mainly use the analysis tool to study manifolds (or more generally Alexandrov space) geometry, topology or complex structure. When a manifold geometry have sufficient symmetry, this is referred to as having manifold Canonical (Canonical) structure. With the canonical structure of the manifold can usually be completely classified, such manifolds overall classification attributed to manifolds canonical decomposition problem. With the three-dimensional closed manifold complete canonical decomposition of Hamilton-Perelman theory of how to carry out a four-dimensional manifold canonical decomposition has been put on the agenda. The main purpose of this project is to try to apply through in-depth analysis of the proper operation and geometric deformation to achieve understanding of the four-dimensional manifold geometry, topology and understanding of a wide range of four-dimensional space-time structure. In the meantime, we intend to study geometric analysis and geometry Gromov's internal relations, in particular the study of geometry Alexandrov space. Through these studies to achieve the four-dimensional structure of the Ricci flow and singularities four-dimensional space of understanding. We also study the flow of non-canonical Kaehler Structure canonical structure and shape on the complex vector bundles. More... »

URL

http://npd.nsfc.gov.cn/projectDetail.action?pid=10831008

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