Remarks on Non-compact Complete Ricci Expanding Solitons
نویسندگان
چکیده
In this paper, we study gradient Ricci expanding solitons (X, g) satisfying Rc = cg +Df, where Rc is the Ricci curvature, c < 0 is a constant, and Df is the Hessian of the potential function f on X . We show that for a gradient expanding soliton (X, g) with non-negative Ricci curvature, the scalar curvature R has at least one maximum point on X , which is the only minimum point of the potential function f . Furthermore, R > 0 on X unless (X, g) is Ricci flat. We also show that there is exponentially decay for scalar curvature for ǫ-pinched complete non-compact expanding solitons.
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