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The curvature estimate of gradient \(\rho\) Einstein soliton. (English) Zbl 1464.53062

Summary: In this paper, we estimate the curvature of the \(\rho\) Einstein soliton with \(0\leq\rho<\frac{1}{2(n-1)}\). We show that the curvature operator is at most polynomial growth if the Ricci curvature is bounded and the volume of the unit ball has a uniform lower bound. Furthermore, for 4 dimensional \(\rho\) Einstein soliton, the curvature operator is bounded if the Ricci curvature is bounded.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53E20 Ricci flows
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