Orthogonal Asymptotic Lines on Surfaces Immersed in \mathbf R ⁴

2006/06/10 by Luis Fernando Mello, Mello, Luis Fernando
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #math.DG #math.DS #msc:53A05 #msc:58C25

paper · pdf · doi:10.48550/arxiv.math/0606245

19 pages

arxiv created 2006/06/10 · arxiv updated 2009/12/01

Abstract

In this paper we study some properties of surfaces immersed in \mathbf R ⁴ whose asymptotic lines are orthogonal. We also analyze necessary and sufficient conditions for the hypersphericity of surfaces in \mathbf R ⁴.

Related

• Geometry of surfaces in \mathbb R⁵ through projections and normal sections
• Principal Mean Curvature Foliations on Surfaces immersed in \mathbb R ⁴
• Blaschke's asymptotic lines of surfaces in R3
• Surfaces close to the Severi lines
• A Cauchy problem for minimal spacelike surfaces in ℝ⁴₂