Anticonformal automorphisms of compact Riemann surfaces

Author:
Robert Zarrow

Journal:
Proc. Amer. Math. Soc. **54** (1976), 162-164

MSC:
Primary 30A46

DOI:
https://doi.org/10.1090/S0002-9939-1976-0404612-7

MathSciNet review:
0404612

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Abstract: We show that an automorphism of prime order of a compact Riemann surface is embeddable if it is the square of an anticonformal automorphism. Also, every embeddable automorphism of odd order of a compact Riemann surface is the square of an orientation reversing selfhomeomorphism.

**[1]**A. M. Garsia,*An embedding of closed Riemann surfaces in Euclidean space*, Comment. Math. Helv.**35**(1961), 93-110. MR**23**#A2890. MR**0125591 (23:A2890)****[2]**R. A. Rüedy,*Embeddings of open Riemann surfaces*, Comment. Math. Helv.**46**(1971), 214-225. MR**46**#3781. MR**0304649 (46:3781)****[3]**-,*Symmetric embeddings of Riemann surfaces*, Discontinuous Groups and Riemann Surfaces, Princeton Univ. Press, Princeton, N.J., 1971, pp. 406-418.**[4]**R. Zarrow,*A canonical form for symmetric and skew symmetric extended symplectic modular matrices with applications to Riemann surface theory*, Trans. Amer. Math. Soc.**204**(1975), 207-227. MR**0407324 (53:11100)**

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DOI:
https://doi.org/10.1090/S0002-9939-1976-0404612-7

Article copyright:
© Copyright 1976
American Mathematical Society