Rigidity of 4-dimensional complete self-shrinkers in ℝ⁵

2022/09/16 by Yi, Chengyang
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.07955

Abstract

We show that any 4-dimensional complete self-shrinker in ℝ⁵ with constant squared norm S of the second fundamental form, f₃=0 and constant f₄ is isometric to ℝ⁴, where h_ij are components of the second fundamental form, S=∑ h_ij², f₃=∑ h_ijh_jkh_ki and f₄=∑ h_ijh_jkh_klh_li. As an application, we obtain a classification result.

Related

• A rigidity theorem of self-expander
• Complete self-shrinkers with constant norm of the second fundamental form
• The rigidity theorems of self shrinkers
• The rigidity theorem for complete Lagrangian self-shrinkers
• The second gap on complete self-shrinkers