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$%A. Melekoğlu, A family of M-surfaces whose automorphism groups act transitively on the mirrors, Rev. Mat. Complut. 13 (2000), no. 1, 163181.%$

A Family of M-Surfaces Whose Automorphism Groups Act Transitively on the Mirrors
Adnan MELEKOĞLU
Adnan Menderes Üniversitesi
Fen-Edebiyat
Fakültesi Matematik Bölümü
09010 Aydin — Turkey

Received: November 11, 1998
Revised: October 18, 1999

ABSTRACT

Let X  be a compact Riemann surface of genus g > 1  . A symmetry T  of X  is an anticonformal involution. The fixed point set of T  is a disjoint union of simple closed curves, each of which is called a mirror of T  . If T  fixes g+ 1  mirrors then it is called an M-symmetry and X  is called an M-surface. If X  admits an automorphism of order g+ 1  which cyclically permutes the mirrors of T  then we shall call X  an M-surface with the M-property. In this paper we investigate those M-surfaces with the M-property and their automorphism groups.

1991 Mathematics Subject Classification: 30F10.