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The Global Property of Generic Conformally Flat Hypersurfaces in R 4

Author

Listed:
  • Yayun Chen

    (Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China)

  • Tongzhu Li

    (Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

A conformally flat hypersurface f : M 3 → R 4 in the four-dimensional Euclidean space R 4 is said to be generic if the hypersurface has three distinct principal curvatures everywhere. In this paper, we study the generic conformally flat hypersurfaces in R 4 using the framework of Möbius geometry. First, we classify locally the generic conformally flat hypersurfaces with a vanishing Möbius form under the Möbius transformation group of R 4 . Second, we investigate the global behavior of the compact generic conformally flat hypersurfaces and give some integral formulas about the Möbius invariant of these hypersurfaces.

Suggested Citation

  • Yayun Chen & Tongzhu Li, 2023. "The Global Property of Generic Conformally Flat Hypersurfaces in R 4," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1435-:d:1098717
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