The Monge-ampère Operator and Geodesics in the Space of Kähler Potentials
نویسنده
چکیده
Let X be an n-dimensional compact complex manifold, L → X a positive holomorphic line bundle, and H the space of positively curved hermitian metrics on L. The purpose of this article is to prove that geodesics in the infinite-dimensional symmetric space H can be uniformly approximated by geodesics in the finite-dimensional symmetric spaces Hk = GL(Nk + 1,C)/U(Nk + 1,C), where Nk + 1 = dim(H(L)). Thus the Hk ⊆ H are becoming flat as k → ∞.
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