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5 votes

Condition for infinite dimensional complex manifold to be Kähler by pullback form

There are three definitions of infinite-dimensional complex manifolds: strong (existence of holomorphic charts), weak (abundance of holomorphic functions) and formal (vanishing of Nijenhuis tensor). T …
Misha Verbitsky's user avatar
10 votes
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Infinite dimensional Riemannian geometry

Lempert, László The Dolbeault complex in infinite dimensions. III. Sheaf cohomology in Banach spaces. Invent. Math. 142 (2000), no. 3, 579-603. Lempert, László The Dolbeault complex in infinite dimen …
Misha Verbitsky's user avatar