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Knots in S 2 x S 1 derived from Sym(2, ℝ)

Sang Lee, Yongdo Lim, Chan-Young Park (2000)

Fundamenta Mathematicae

We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in S 2 × S 1 and show that these knots or links have certain types of symmetry of period 2.

Kobayashi-Royden vs. Hahn pseudometric in ℂ²

Witold Jarnicki (2000)

Annales Polonici Mathematici

For a domain D ⊂ ℂ the Kobayashi-Royden ϰ and Hahn h pseudometrics are equal iff D is simply connected. Overholt showed that for D n , n ≥ 3, we have h D ϰ D . Let D₁, D₂ ⊂ ℂ. The aim of this paper is to show that h D × D iff at least one of D₁, D₂ is simply connected or biholomorphic to ℂ 0. In particular, there are domains D ⊂ ℂ² for which h D ϰ D .

K-subanalytic rectilinearization and uniformization

Artur Piękosz (2003)

Open Mathematics

We prove rectilinearization and uniformization theorems for K-subanalytic (∝anK-definable) sets and functions using the Lion-Rolin formula. Parallel reasoning gives standard results for the subanalytic case.

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