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On a generalization of the Liouville conformal theorem to general rigid geometric structures

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Abstract

For any \(n\ge 3\), the classical Liouville theorem asserts that any local conformal diffeomorphism defined on a connected open subset of \({\mathbb {S}}^n\) can be uniquely extended to a M\(\ddot{\mathrm{o}}\)bius transformation. In this article, we formulate and prove a generalization of this theorem to general rigid geometric structures.

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Acknowledgements

The author sincerely thanks the referee for the numerous and valuable suggestions. The author also thanks Becky Scott and Daniel Ehmann for their support in English.

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  1. Département de Mathématiques, CY Cergy Paris université, 2, avenue Adolphe Chauvin, 95302, Cergy Pontoise Cedex, France

    Yong Fang

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  1. Yong Fang
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Correspondence to Yong Fang.

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Fang, Y. On a generalization of the Liouville conformal theorem to general rigid geometric structures. Geom Dedicata 214, 139–155 (2021). https://doi.org/10.1007/s10711-021-00608-z

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