Abstract
We obtain the exact values of the systoles of these hyperbolic surfaces of genus g with cyclic symmetry of the maximum order and the next maximum order. Precisely, for the genus g hyperbolic surface with order 4g + 2 cyclic symmetry, the systole is \(\left( {1 + \cos {{\rm{\pi }} \over {2g + 1}} + \cos {{2{\rm{\pi }}} \over {2g + 1}}} \right)\) when g ⩾ 7, and for the genus g hyperbolic surface with order 4g cyclic symmetry, the systole is \(\left( {1 + 2\cos {{\rm{\pi }} \over {2g}}} \right)\) when g ⩾ 4.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 11711021). The authors thank Professor Ursula Hamenstädt for helpful communication.
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Bai, S., Gao, Y. & Wang, S. Systoles of hyperbolic surfaces with big cyclic symmetry. Sci. China Math. 64, 421–442 (2021). https://doi.org/10.1007/s11425-019-1655-8
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DOI: https://doi.org/10.1007/s11425-019-1655-8