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Abstract |
Kähler metrics are a special class of Riemannian metrics, defined on complex manifolds, and
locally expressed as the (complex) Hessian of a potential. Kähler metrics with constant Ricci
curvature are called Kähler-Einstein, and come in three flavors, according to the curvature
sign. I will review Aubin and Yau's classical existence and uniqueness results in the case of
negative and zero curvature (Calabi-Yau metrics), and describe some aspects of the Yau-
Tian-Donaldson conjecture, solved a few years ago, and which solves the existence problem
in the case of positive curvature (Fano manifolds). |
