scholarly journals Supersymmetric nonlinear sigma models on Ricci-flat Kähler manifolds with O(N) symmetry

2001 ◽  
Vol 515 (3-4) ◽  
pp. 421-425 ◽  
Author(s):  
Kiyoshi Higashijima ◽  
Tetsuji Kimura ◽  
Muneto Nitta
Keyword(s):  
Sigma Models ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Ricci Flat ◽  
Nonlinear Sigma Models

scholarly journals New extended superconformal sigma models and quaternion Kähler manifolds

2009 ◽  
Vol 2009 (09) ◽  
pp. 119-119 ◽  
Author(s):  
Sergei M Kuzenko ◽  
Ulf Lindström ◽  
Rikard von Unge
Keyword(s):  
Sigma Models ◽  
Kähler Manifolds ◽  
Kahler Manifolds

scholarly journals A C0-estimate for the parabolic Monge–Ampère equation on complete non-compact Kähler manifolds

2009 ◽  
Vol 146 (1) ◽  
pp. 259-270 ◽  
Author(s):  
Albert Chau ◽  
Luen-Fai Tam
Keyword(s):  
Ricci Flow ◽  
Kähler Manifolds ◽  
Main Step ◽  
Kahler Manifolds ◽  
Compact Sets ◽  
Ricci Flat ◽  
Long Time ◽  
Flat Manifolds ◽  
Monge Ampere ◽  
Invent Math

AbstractIn this article we study the Kähler–Ricci flow, the corresponding parabolic Monge–Ampère equation and complete non-compact Kähler–Ricci flat manifolds. Our main result states that if (M,g) is sufficiently close to being Kähler–Ricci flat in a suitable sense, then the Kähler–Ricci flow has a long time smooth solution g(t) converging smoothly uniformly on compact sets to a complete Kähler–Ricci flat metric on M. The main step is to obtain a uniform C0-estimate for the corresponding parabolic Monge–Ampère equation. Our results on this can be viewed as parabolic versions of the main results of Tian and Yau [Complete Kähler manifolds with zero Ricci curvature. II, Invent. Math. 106 (1990), 27–60] on the elliptic Monge–Ampère equation.

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