Yamabe metrics with non parallel Ricci tensor
by
A. Raouf Chouikha
University of Paris-Nord, France

Oral Communication

We descrive metrics with constant scalar curvature and with Ricci tensor non parallel. In the compact case of the Riemannian manifolds and if the scalar curvature is constant positive, these metrics have been classified by A. Derdzinski .

In particular, for the Fowler metrics which belong to the conformal class [dt²+d\xi²] of the Riemannian product  S¹×S^n-1 : a circle of length  T  crossed with the standard (n-1)-dimensional sphere, we have shown these metrics have a harmonic Riemannian curvature and a non parallel Ricci tensor, except for the cylindric one. Thus, it appears a natural link between Fowler metrics nd the Derdzinski metrics, which are warped products   dt² + f²(t) d\xi² .  These two families actually differ by conformal transformations.

We also examine the curvature of the asymptotic Fowler metrics which are complete Yamabe metrics on  Sⁿ -\Lambda_k ,  where \Lambda_k  is a finite set of k points in  Sⁿ,  and  k >= 2.  We show that their Ricci tensor are also non parallel except for the cylindric one.

Date received: June 2, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafh-08.