Work

Möbius geometry of locally conformal flat hypersurfaces

Year: 2024

Type: article

Abstract: In this paper, we consider the Möbius geometry of locally conformal flat hypersurfaces. First, we prove that any locally conformal flat hypersurface in the sphere S n + 1 ( n ≥ 4 ) is a canal hypersurface, which is the envelope of a one-parameter family of principal curvature hyperspheres . Conversely, canal hypersurfaces in S n + 1 ( n ≥ 3 ) without umbilical points are locally conformal flat. Finally, by applying the maximum principle, we show that a compact umbilical points hypersurface with isotropic Blaschke tensor in S n + 1 ( n ≥ 3 ) is Möbius equivalent to a compact minimal hypersurface with constant scalar curvature in S n + 1 .

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2024.128825

Authors: Fengjiang Li, Zhen Guo

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,100