The preservability of the curvature-adaptedness along the mean curvature flow

2020/12/10 by Naoyuki Koike, Koike, Naoyuki
Mathematics · Physics and Astronomy · #53C40 #53C44 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2012.05864

openalex publication_date 2020/12/10 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the preservability of the curvature-adaptedness along the mean curvature flow starting from a compact curvature-adapted hypersurface in locally symmetric spaces, where the curvature-adaptedness means that the shape operator and the normal Jacobi operator of the hypersurface commute.

Related

• Non-preserved curvature conditions under constrained mean curvature flows
• Mean curvature flow in higher codimension
• Gaussian Mean curvature flow
• The mean curvature flow of submanifolds of high codimension
• Mean curvature flow of mean convex hypersurfaces