New York Journal of Mathematics
Volume 23 (2017) 1739-1749


Peng Wu

Curvature decompositions on Einstein four-manifolds

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Published: November 27, 2017
Keywords: Einstein four-manifolds, standard curvature decomposition, duality curvature decomposition, Berger curvature decomposition, k-positive curvature operator, positive sectional curvature, positive isotropic curvature.
Subject: Primary 53C25.

For Einstein four-manifolds with positive scalar curvature, we investigate relations among various positivity conditions on the curvature tensor, some of which are of great importance in the study of the Ricci flow. These relations suggest possible new ideas to study the well-known rigidity conjecture for positively curved Einstein four-manifolds.

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Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, China