2011 | OriginalPaper | Chapter
Einstein metrics and preserved curvature conditions for the Ricci flow
Author : Simon Brendle
Published in: Complex and Differential Geometry
Publisher: Springer Berlin Heidelberg
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Let
C
be a cone in the space of algebraic curvature tensors. Moreover, let
(M,g)
be a compact Einstein manifold with the property that the curvature tensor of
(M,g)
lies in the interior of the cone
C
at each point on
M
. We show that
(M,g)
has constant sectional curvature if the cone
C
satisfies certain structure conditions.