Riemannian manifolds that are scalar flat but not ricci flat - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T18:07:53Z http://mathoverflow.net/feeds/question/67216 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/67216/riemannian-manifolds-that-are-scalar-flat-but-not-ricci-flat Riemannian manifolds that are scalar flat but not ricci flat atreyee 2011-06-08T06:40:25Z 2011-06-20T02:27:12Z <p>What are the examples of Riemannian manifolds that have zero scalar curvature but non zero ricci curvature? Is there any sort of classification of such manifolds?</p> http://mathoverflow.net/questions/67216/riemannian-manifolds-that-are-scalar-flat-but-not-ricci-flat/68258#68258 Answer by Viktor Bundle for Riemannian manifolds that are scalar flat but not ricci flat Viktor Bundle 2011-06-20T02:27:12Z 2011-06-20T02:27:12Z <p>To generalize Anton's comment a little, I should add that with the appropriate choice of $l$ and $k$, the product manifold $S^l \times N^k$ will have the property that you are looking for, where $N^k$ has hyperbolic $k$-dimensional half-space space as its cover. You can find the formulas for all of the geometric quantities related to these sorts of products in Chang, Han, Yang "On a class of locally conformally flat manifolds". This particular combination of manifolds can be used to construct many examples of manifolds with interesting curvature. </p>