Metric connections in projective differential geometry

Authors :: Eastwood, Michael
Matveev, Vladimir S.
Source :: Symmetries and Overdetermined Systems of Partial Differential Equations (Minneapolis, MN, 2006), 339--351, IMA Vol. Math. Appl., 144(2007), Springer, New York
Publication Year :: 2008
Abstract: We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, 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.<br />Comment: 10 pages

Subjects :: Mathematics - Differential Geometry
Mathematics - Analysis of PDEs
53A20

Database :: arXiv
Journal :: Symmetries and Overdetermined Systems of Partial Differential Equations (Minneapolis, MN, 2006), 339--351, IMA Vol. Math. Appl., 144(2007), Springer, New York
Publication Type :: Report
Accession number :: edsarx.0806.3998
Document Type :: Working Paper

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