2009/05/27 by Georgi Ganchev, Ganchev, Georgi, Velichka Milousheva +1 · 2 citations
Computer Science · Engineering · Mathematics · #53A07 #53A10 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #math.DG #msc:53A07 #msc:53A10
paper · pdf · doi:10.48550/arxiv.0905.4453
13 pages
arxiv created 2009/05/27 · openalex publication_date 2009/05/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
At any point of a surface in the four-dimensional Euclidean space we consider the geometric configuration consisting of two figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We show that the basic geometric classes of surfaces in the four-dimensional Euclidean space, determined by conditions on their invariants, can be interpreted in terms of the properties of the two geometric figures. We give some non-trivial examples of surfaces from the classes in consideration.