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

Liu, Gang

Asian J. Math. 18, No. 1, 69-100 (2014).

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.

Reviewer: Zbigniew Olszak (Wrocław)

MSC:

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

Keywords:

Kähler manifold; comparison theorem