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تسجيل مستخدم جديدRigidity theorems of complete Kahler-Einstein manifolds and complex space forms
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We derive some elliptic differential inequalities from the Weitzenbock formulas for the traceless Ricci tensor of a Kahler manifold with constant scalar curvature and the Bochner tensor of a Kahler-Einstein manifold respectively. Using elliptic estimates and maximum principle, some $L^p$ and $L^infty $ pinching results are established to characterize Kahler-Einstein manifolds among Kahler manifolds with constant scalar curvature, and others are given to characterize complex space forms among Kahler-Einstein manifolds. Finally, these pinching results may be combined to characterize complex space forms among Kahler manifolds with constant scalar curvature.
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