| EPSRC Reference: |
GR/M18355/01 |
| Title: |
RANK AND SYMMETRY IN RIEMANNIAN GEOMETRY |
| Principal Investigator: |
Berndt, Professor J |
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| Department: |
Mathematics |
| Organisation: |
University of Hull |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 February 1999 |
Ends: |
31 May 2001 |
Value (£): |
52,496
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Symmetric spaces play a central role in geometry and analysis. A fundamental problem is to find sufficient criteria in order that a Riemannian manifold is isometric or locally isometric to some symmetric space. Several important criteria are known by using the concept of rank, which measures the amount of flatness of a Riemannian manifold.These so-called rank rigidity theorems usually involve global assumptions on the geometry or topology of manifold, for instances homogeneity or compactness. We plan to develop a method for investigating rigidity using only local geometry, to obtain new local rigidity results, and thereby to improve known global ones. Our idea to approach this based on two kinds of objects, infinitesimal models and flats. Infinitesimal models represent the tangent space with its metric and cirvature tensor at a fixed point. From these algebraic objects one can read off much information. For instance, local homogeneity can be encoded entirely in properties of an infinitesimal model. The flats are fundamental for the geometric and algebraic theory of symmetric spaces. We plan to encode the structure of the flats in symmetric spaces into infinitesimal models, and then use these infinitesimal data as the basis for rigidity investigations.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.hull.ac.uk |