Displaying similar documents to “Nash Manifolds”

A short introduction to shadows of 4-manifolds

Francesco Costantino (2005)

Fundamenta Mathematicae

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We give a self-contained introduction to the theory of shadows as a tool to study smooth 3-manifolds and 4-manifolds. The goal of the present paper is twofold: on the one hand, it is intended to be a shortcut to a basic use of the theory of shadows, on the other hand it gives a sketchy overview of some of the most recent results on shadows. No original result is proved here and most of the details of the proofs are left out.

Khintchine types of translated coordinate hyperplanes

Felipe A. Ramírez (2015)

Acta Arithmetica

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There has been great interest in developing a theory of "Khintchine types" for manifolds embedded in Euclidean space, and considerable progress has been made for curved manifolds. We treat the case of translates of coordinate hyperplanes, decidedly flat manifolds. In our main results, we fix the value of one coordinate in Euclidean space and describe the set of points in the fiber over that fixed coordinate that are rationally approximable at a given rate. We identify translated coordinate...

Oka manifolds: From Oka to Stein and back

Franc Forstnerič (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989. In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent...

On stability of 3-manifolds

Sławomir Kwasik, Witold Rosicki (2004)

Fundamenta Mathematicae

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We address the following question: How different can closed, oriented 3-manifolds be if they become homeomorphic after taking a product with a sphere? For geometric 3-manifolds this paper provides a complete answer to this question. For possibly non-geometric 3-manifolds, we establish results which concern 3-manifolds with finite fundamental group (i.e., 3-dimensional fake spherical space forms) and compare these results with results involving fake spherical space...

Products of open manifolds with ℝ

Craig R. Guilbault (2007)

Fundamenta Mathematicae

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We present a characterization of those open n-manifolds (n ≥ 5) whose products with the real line are homeomorphic to interiors of compact (n+1)-manifolds with boundary.

Generalized Kählerian manifolds and transformation of generalized contact structures

Habib Bouzir, Gherici Beldjilali, Mohamed Belkhelfa, Aissa Wade (2017)

Archivum Mathematicum

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The aim of this paper is two-fold. First, new generalized Kähler manifolds are constructed starting from both classical almost contact metric and almost Kählerian manifolds. Second, the transformation construction on classical Riemannian manifolds is extended to the generalized geometry setting.