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On a compact n -dimensional manifold M , it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar… Click to show full abstract
On a compact n -dimensional manifold M , it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, we prove the Besse conjecture for compact manifolds with pinched Weyl curvature. Moreover, we shall conclude that such a conjecture is true if its Weyl curvature tensor and the Kulkarni-Nomizu product of Ricci curvature are orthogonal.
Keywords:
compact manifolds;
conjecture;
besse conjecture;
manifolds pinched;
conjecture compact;
curvature
Journal Title: Archiv der Mathematik
Year Published: 2020
Link to full text (if available)
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Journal Title: Archiv der Mathematik
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!