1. Prescribing symmetric functions of the eigenvalues of the Ricci tensor
- Author
-
Matthew J. Gursky and Jeff A. Viaclovsky
- Subjects
Weyl tensor ,Pure mathematics ,Riemann curvature tensor ,Curvature of Riemannian manifolds ,010102 general mathematics ,Mathematical analysis ,Ricci flow ,01 natural sciences ,symbols.namesake ,Mathematics (miscellaneous) ,0103 physical sciences ,symbols ,Symmetric tensor ,Ricci decomposition ,Mathematics::Differential Geometry ,010307 mathematical physics ,0101 mathematics ,Statistics, Probability and Uncertainty ,Metric tensor (general relativity) ,Ricci curvature ,Mathematics - Abstract
We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric.
- Published
- 2007
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