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

K-analytic versus Ccm-analytic Sets in Nonstandard Compact Complex Manifolds

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.

Analytic fields on compact balanced Hermitian manifolds

On a Hermitian manifold we construct a symmetric (1, 1)tensor H using the torsion and the curvature of the Chern connection. On a compact balanced Hermitian manifold we find necessary and sufficient conditions in terms of the tensor H for a harmonic 1-form to be analytic and for an analytic 1form to be harmonic. We prove that if H is positive definite then the first Betti number b1 = 0 and the ...

Neighborhoods of Analytic Varieties in Complex Manifolds

Baker-sprindžuk Conjectures for Complex Analytic Manifolds

The circle of problems that the present paper belongs to dates back to the 1930s, namely, to K. Mahler’s work on a classification of transcendental real and complex numbers. For a polynomial P (x) = a0 + a1x + · + anx n ∈ Z[x], let us denote by hP the height of P , that is, hP def = maxi=0,...,n |ai|. It can be easily shown using Dirichlet’s Principle that for any z ∈ C and any n ∈ N there exis...

Complex Analytic Manifolds without Countable Base

1. It has been shown by Radó3 that every Riemann surface satisfies Hausdorff's second countability axiom. In the same paper Radó gives a construction due to Prüfer of a real 2-dimensional locally Euclidean space whose open sets do not have a countable base. The purpose of this paper is to confirm a conjecture of Bochner that there exist non second-countable complex manifolds of complex dimensio...