Classification of Punctures on Complete Flat Surfaces

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.

Keywords:

Flat surface, regular puncture, irregular puncture conical singularities,

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International Electronic Journal of Geometry-Cover

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2008
Yayıncı: Prof.Dr. H.Hilmi Hacısalioğlu

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