RMC - Vol. 13, Num. 1 - Adnan Melekoğlu

Full paper in PDF:
$%A. Melekoğlu, A family of M-surfaces whose automorphism groups act transitively on the mirrors, Rev. Mat. Complut. 13 (2000), no. 1, 163–181.%$

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.