Complex analytic geometry of complex parallelizable manifolds

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...

Geometry of product complex Cartan manifolds

In this paper we consider the product of two complex Cartan manifolds, the outcome being a class of product complex Cartan spaces. Then, we study the relationships between the geometric objects of a product complex Cartan space and its components, (e.g. Chern-Cartan complex nonlinear connection, Cartan tensors). By means of these, we establish the necessary and sufficient conditions under which...

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...

Lectures on complex geometry, Calabi–Yau manifolds and toric geometry

These are introductory lecture notes on complex geometry, Calabi–Yau manifolds and toric geometry. We first define basic concepts of complex and Kähler geometry. We then proceed with an analysis of various definitions of Calabi–Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi–Yau manifolds in two different ways; as hypersurfaces in to...