The Global Property of Generic Conformally Flat Hypersurfaces in R 4

Yayun Chen and Tongzhu Li ()
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Yayun Chen: Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
Tongzhu Li: Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2023, vol. 11, issue 6, 1-13

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.

Keywords: generic conformally flat hypersurface; Möbius metric; Möbius form; Möbius curvature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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