2023/03/07 by Alexandre Paiva Barreto, Barreto, Alexandre Paiva, Fernando Gasparotto +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2303.03623
In this article we fully classify regular tubular surfaces in Euclidean, Lorentzian and hyperbolic 3-spaces whose Gaussian and mean curvatures K and H verify a polynomial relation. More precisely, we determine the set S(Q) of all regular tubular surfaces whose curvatures verify a given polynomial relation Q(K,H)=0, and the set Q(S) of all polynomial relations vanished by the curvatures of a given tubular surface S.