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

  • Author(s): Qing, J
  • Wang, C
  • Zhong, J
  • et al.
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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