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Kähler manifolds with Ricci curvature lower bound. (English) Zbl 1306.53023

Author’s abstract: On Kähler manifolds with Ricci curvature bounded from below, we establish some theorems which are counterparts of some classical theorems in Riemannian geometry, for example, Bishop-Gromov’s relative volume comparison, Bonnet-Myers theorem, and Yau’s gradient estimate for positive harmonic functions. The tool is a Bochner type formula reflecting the Kähler structure.

MSC:

53C20 Global Riemannian geometry, including pinching
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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