Metric connections in projective differential geometry
Date
2008
Authors
Eastwood, Michael George
Matveev, Vladimir
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Book chapter
Citation
Sysmmetries and Overdetermined Systems of Partial Differential Equations / Michael Eastwood and Willard Miller (eds.):pp.339-350
Statement of Responsibility
Michael Eastwood and Vladimir Matveev
Conference Name
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.
School/Discipline
School of Mathematical Sciences