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Displaying similar documents to “Tri-analytic Subvarieties of Hyperkähler Manifolds.”

K-analytic versus ccm-analytic sets in nonstandard compact complex manifolds

Rahim Moosa, Sergei Starchenko (2008)

Fundamenta Mathematicae

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It is shown that in an elementary extension of a compact complex manifold M, the K-analytic sets (where K is the algebraic closure of the underlying real closed field) agree with the ccm-analytic sets if and only if M is essentially saturated. In particular, this is the case for compact Kähler manifolds.

On nonimbeddability of Hartogs figures into complex manifolds

E. Chirka, S. Ivashkovich (2006)

Bulletin de la Société Mathématique de France

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We prove the impossibility of imbeddings of Hartogs figures into general complex manifolds which are close to an imbedding of an analytic disc attached to a totally real collar. Analogously we provide examples of the so called thin Hartogs figures in complex manifolds having no neighborhood biholomorphic to an open set in a Stein manifold.

Grauert's theorem for subanalytic open sets in real analytic manifolds

Daniel Barlet, Teresa Monteiro Fernandes (2011)

Studia Mathematica

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By an open neighbourhood in ℂⁿ of an open subset Ω of ℝⁿ we mean an open subset Ω' of ℂⁿ such that ℝⁿ ∩ Ω' = Ω. A well known result of H. Grauert implies that any open subset of ℝⁿ admits a fundamental system of Stein open neighbourhoods in ℂⁿ. Another way to state this property is to say that each open subset of ℝⁿ is Stein. We shall prove a similar result in the subanalytic category: every subanalytic open subset in a paracompact real analytic manifold M admits a fundamental system...

The Lie group of real analytic diffeomorphisms is not real analytic

Rafael Dahmen, Alexander Schmeding (2015)

Studia Mathematica

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We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense...