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Curvature estimates for gradient expanding Ricci solitons
Liangdi Zhang 대한수학회 2021 대한수학회보 Vol.58 No.3
In this paper, we investigate the curvature behavior of complete noncompact gradient expanding Ricci solitons with nonnegative Ricci curvature. For such a soliton in dimension four, it is shown that the Riemann curvature tensor and its covariant derivatives are bounded. Moreover, the Ricci curvature is controlled by the scalar curvature. In higher dimensions, we prove that the Riemann curvature tensor grows at most polynomially in the distance function.
Rigidity of gradient shrinking and expanding Ricci solitons
Fei Yang,Liangdi Zhang 대한수학회 2017 대한수학회보 Vol.54 No.3
In this paper, we prove that a gradient shrinking Ricci soliton is rigid if the radial curvature vanishes and the second order divergence of Bach tensor is non-positive. Moreover, we show that a complete non-compact gradient expanding Ricci soliton is rigid if the radial curvature vanishes, the Ricci curvature is nonnegative and the second order divergence of Bach tensor is nonnegative.
RIGIDITY OF GRADIENT SHRINKING AND EXPANDING RICCI SOLITONS
Yang, Fei,Zhang, Liangdi Korean Mathematical Society 2017 대한수학회보 Vol.54 No.3
In this paper, we prove that a gradient shrinking Ricci soliton is rigid if the radial curvature vanishes and the second order divergence of Bach tensor is non-positive. Moreover, we show that a complete non-compact gradient expanding Ricci soliton is rigid if the radial curvature vanishes, the Ricci curvature is nonnegative and the second order divergence of Bach tensor is nonnegative.