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https://hdl.handle.net/2440/54409
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Type: | Book chapter |
Title: | Metric connections in projective differential geometry |
Author: | Eastwood, Michael George Matveev, Vladimir |
Citation: | Sysmmetries and Overdetermined Systems of Partial Differential Equations / Michael Eastwood and Willard Miller (eds.):pp.339-350 |
Publisher: | Springer |
Issue Date: | 2008 |
Series/Report no.: | The IMA Volumes in Mathematics and its Applications ; 144 |
ISBN: | 9780387738314 |
School/Discipline: | School of Mathematical Sciences |
Statement of Responsibility: | Michael Eastwood and Vladimir Matveev |
Abstract: | We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikeš, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sections of a certain vector bundle with connection. This vector bundle and its connection are derived from the Cartan connection of the underlying projective structure. |
Keywords: | projective differential geometry; metric connection; tractor |
DOI: | 10.1007/978-0-387-73831-4_16 |
Description (link): | http://www.springer.com/math/dyn.+systems/book/978-0-387-73830-7 |
Appears in Collections: | Mathematical Sciences publications |
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