2019/05/28 by Ronaldo F. de Lima, de Lima, Ronaldo F., Pedro Roitman +1
Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometry #Mathematics #Product (mathematics) #Pure mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.1905.12026
The results will be included in a different paper
openalex publication_date 2019/05/28 · arxiv created 2019/06/22 · arxiv updated 2019/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a complete Riemannian manifold Mn and let Σn be an orientable hypersurface of the product manifold M×ℝ endowed with its standard product metric ⟨ , ⟩. Let ∇ξ denote the gradient of the height function ξ of Σ. In this note, we characterize the hypersurfaces Σ which have ∇ξ as a principal direction. Our approach is based on the work of R. Tojeiro, who considered the case where M is a constant sectional curvature space form.