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A NEW CHARACTERIZATION OF WIMAN SURFACES

Part of: Graph theory

Published online by Cambridge University Press:  27 July 2009

ADNAN MELEKOĞLU
ADNAN MELEKOĞLU*
Affiliation:
Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, 09010 Aydın, Turkey (email: amelekoglu@hotmail.com)
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Abstract

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Let ℳ be a regular map of genus g>1 and X be the underlying Riemann surface. A reflection of ℳ fixes some simple closed curves on X, which we call mirrors. Each mirror passes through at least two of the geometric points (vertices, face-centers and edge-centers) of ℳ. In this paper we study the surfaces which contain mirrors passing through just two geometric points, and show that only Wiman surfaces have this property.

Keywords

Riemann surfaceWiman surfaceregular mapgeometric pointreflectionpattern

MSC classification

Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 3 , December 2009 , pp. 360 - 368
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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