Abstract
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.
Mathematics Subject Classification (2010) Primary 53C25. Secondary 53C24, 53C44.
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Brendle, S. (2011). Einstein metrics and preserved curvature conditions for the Ricci flow. In: Ebeling, W., Hulek, K., Smoczyk, K. (eds) Complex and Differential Geometry. Springer Proceedings in Mathematics, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20300-8_4
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DOI: https://doi.org/10.1007/978-3-642-20300-8_4
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