UC Santa Cruz
Scalar Invariants of surfaces in conformal 3-sphere via Minkowski
- Author(s): Qing, J
- Wang, C
- Zhong, J
- et al.
Published Web Locationhttps://doi.org/10.2140/pjm.2017.286.153
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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