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arXiv · 1602.08076

Scalar Invariants of surfaces in conformal 3-sphere via Minkowski spacetime

Jie Qing·Changping Wang·Jingyang Zhong
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Abstract

For a surface in 3-sphere, by identifying the conformal round 3-sphere as the projectivized positive light cone in Minkowski 5-spacetime, we use the conformal Gauss map and the conformal transform to construct the associate homogeneous 4-surface in Minkowski 5-spacetime. We then derive the local fundamental theorem for a surface in conformal round 3-sphere from that of the associate 4-surface in Minkowski 5-spacetime. More importantly, following the idea of Fefferman and Graham, we construct local scalar invariants for a surface in conformal round 3-sphere. One distinct feature of our construction is to link the classic work of Blaschke to the works of Bryan and Fefferman-Graham.

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Jie Qing, Changping Wang, Jingyang Zhong. 2016-02-25. Scalar Invariants of surfaces in conformal 3-sphere via Minkowski spacetime. https://doi.org/10.2140/pjm.2017.286.153

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