Prime order automorphisms of Klein surfaces representable by rotations of the euclidean space

Antonio F. Costa; Cam Van Quach Hongler

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arXiv · 1010.0172

Prime order automorphisms of Klein surfaces representable by rotations of the euclidean space

Antonio F. Costa·Cam Van Quach Hongler

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Abstract

Let S be a bordered orientable Klein surface and p a prime. Assume that f is an order p automorphism of S. In this work we obtain the conditions on the topological type of (S,f) to be conformally equivalent to (S',f') where S' is a bordered orientable Klein surface embedded in the Euclidean space and f' is the restriction to S' of a prime order rotation. We represent two famous automorphisms using rotations of R^4 and S^4 : the order seven automorphisms of the Klein quartic and the Wiman surface.

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BibTeX RIS

Antonio F. Costa, Cam Van Quach Hongler. 2010-10-15. Prime order automorphisms of Klein surfaces representable by rotations of the euclidean space. https://arxiv.org/abs/1010.0172

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