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Dergiler / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 2

Classification of Punctures on Complete Flat Surfaces

İsmail SAĞLAM
Sayfa
266–276
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We show that there are uncountably many modification-equivalence classes of punctures on flat surfaces.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We investigate the behavior of a complete flat metric on a surface near a puncture.
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Temel Bulgular & Veri:We prove that there are punctures which are not regular if and only if the curvature at the puncture is $4\pi$.
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Sonuç & Katkı:We show that there are uncountably many modification-equivalence classes of punctures on flat surfaces.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Flat surface · regular puncture · irregular puncture

Abstract

We investigate the behavior of a complete flat metric on a surface near a puncture. We call a puncture on a flat surface regular if it has a neighborhood which is isometric to that of a point at infinity of a cone. We prove that there are punctures which are not regular if and only if the curvature at the puncture is $4\pi$. We classify irregular punctures of a flat surface up to modification equivalence, where two punctures are called modification-equivalent if they have isometric neighborhoods. We show that there are uncountably many modification-equivalence classes of punctures on flat surfaces.

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Bu Makaleye Atıf Yap

SAĞLAM, İ. (2022). Classification of Punctures on Complete Flat Surfaces. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 2, 266–276. https://ajindex.com/articles/539574

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