scholarly journals POSITIVITY OF RICCI CURVATURE UNDER THE KÄHLER–RICCI FLOW

2006 ◽  
Vol 08 (01) ◽  
pp. 123-133 ◽  
Author(s):  
DAN KNOPF
Keyword(s):  
Ricci Curvature ◽  
Ricci Flow ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bounded Curvature ◽  
Complex Dimension

In each complex dimension n ≥ 2, we construct complete Kähler manifolds of bounded curvature and non-negative Ricci curvature whose Kähler–Ricci evolutions immediately acquire Ricci curvature of mixed sign.

Holomorphic Functions on a Class of Kähler Manifolds With Nonnegative Curvature, I

2020 ◽  
Author(s):  
Bo Yang
Keyword(s):  
Asymptotic Behavior ◽  
Ricci Curvature ◽  
Ricci Flow ◽  
Polynomial Growth ◽  
Holomorphic Functions ◽  
Nonnegative Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Nonnegative Ricci Curvature

Abstract In this paper, we consider holomorphic functions of polynomial growth on complete Kähler manifolds with nonnegative curvature. We explain how their growth orders are related to the asymptotic behavior of Kähler–Ricci flow. The main result is to determine minimal orders of holomorphic functions on gradient Kähler–Ricci expanding solitons with nonnegative Ricci curvature.

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