Bull. Korean Math. Soc. 2021; 58(3): 537-557
Online first article May 10, 2021 Printed May 31, 2021
https://doi.org/10.4134/BKMS.b190805
Copyright © The Korean Mathematical Society.
Liangdi Zhang
Yanqi Lake Beijing Institute of Mathematical Sciences and Applications
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.
Keywords: Curvature estimate, gradient expanding Ricci soliton, nonnegative Ricci curvature
MSC numbers: Primary 53C21, 53C25
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd