2017/10/16 by Kentaro Saji, Honda, Atsufumi, Saji, Kentaro
Mathematics · Medicine · #53A04 (Secondary) #53A05 #57R45 (Primary) #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Ophthalmology and Eye Disorders
paper · pdf · doi:10.48550/arxiv.1710.06014
openalex created_date 2016/06/24 · openalex publication_date 2017/10/16 · openalex updated_date 2026/07/28
We introduce two invariants called the secondary cuspidal curvature and the bias on 5/2-cuspidal edges, and investigate their basic properties. While the secondary cuspidal curvature is an analog of the cuspidal curvature of (ordinary) cuspidal edges, there are no invariants corresponding to the bias. We prove that the product (called the secondary product curvature) of the secondary cuspidal curvature and the limiting normal curvature is an intrinsic invariant. Using this intrinsity, we show that any real analytic 5/2-cuspidal edges with non-vanishing limiting normal curvature admits non-trivial isometric deformations, which provide the extrinsity of various invariants.