2019/11/11 by Ady Cambraia, Cambraia, Ady, Abigail Folha +3
Engineering · Mathematics · #3D Shape Modeling and Analysis #53C30 #53C42 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1911.04275
openalex publication_date 2019/11/11 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
In this article we classify the totally umbilical surfaces which are immersed into a wide class of Riemannian manifolds having a structure of warped product, more precisely, we show that a totally umbilical surface immersed into the warped product \mathbbM(κ)f× I (here, \mathbbM(κ) denotes the 2-dimensional space form, having constant curvature κ, I an interval and f the warping function) is invariant by an one-parameter group of isometries of the ambient space. We also find the first integral of the ordinary differential equation that the profile curve satisfies (we mean, the curve which generates a invariant totally umbilical surface). Moreover, we construct explicit examples of totally umbilical surfaces, invariant by one-parameter group of isometries of the ambient space, by considering certain non-trivial warping function.