Metric Connections in Projective Differential Geometry

  • Michael Eastwood
  • Vladimir Matveev
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 144)


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.

Key words

Projective differential geometry metric connection tractor 

AMS(M0S) subject classifications

Primary 53A20 Secondary 58570 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Michael Eastwood
    • 1
  • Vladimir Matveev
    • 2
  1. 1.Department of MathematicsUniversity of AdelaideAustralia
  2. 2.Mathematisches Institut, Fakultät für Mathematik und InformatikFriedrich-Schiller-Universität JenaJenaGermany

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