We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham e-Theses
You are in:

Harmonic Riemannian manifolds

Carpenter, Paul (1980) Harmonic Riemannian manifolds. Doctoral thesis, Durham University.



In this thesis work is described that arose out of a study of harmonic Riemannian manifolds. A definition of harmonicity is given and from this it is shown how the Ledger conditions on the curvature of a harmonic manifold may be derived in principle and the first four are written down. The first three Ledger conditions are put into local co-ordinate form and simpler conditions are derived, the most important being the super-Einstein condition. The idea of the Schur property is also introduced. The mean-value work of Gray and Willmore is described and extended as far as the r(^8) term under some simplifying conditions. Finally there is an investigation of the extent to which the compact classical simple Lie groups with bi-invariant metrics can satisfy Ledger’s first three conditions.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Thesis Date:1980
Copyright:Copyright of this thesis is held by the author
Deposited On:18 Sep 2013 15:34

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitter