← Back to Search
Kähler-Einstein Metrics With Non-positive Scalar Curvature
Published 2000 · Mathematics
Reduce the time it takes to create your bibliography by a factor of 10 by using the world’s favourite reference manager
Time to take this seriously.
We have seen that the Ricci curvature represents the first Chern class. In this section, we will consider the converse problem, namely, given a Kahler class [ω] ∈ H2 (M, ℝ) ∩ H1,2 (M, ℂ) on a compact Kahler manifold M and any form Ω representing the first Chern class, can we find a metric ω ∈ [ω] such that Ric(ω) = Ω? This is known as the Calabi conjecture and it was solved by Yau in 1976. We will state it here as a theorem and refer to it as the Calabi-Yau Theorem.