Singular points of equiangular webs
Abstract
We study equiangular $n$-webs on surfaces, where $n$ direction fields are equally spaced in angle at each point away from singular points. Using complex numbers, we express such webs by binary differential equations of the form $A\,dz^n + \ols{A}\,d\ols{z}^n = 0$, and investigate their singularities via the local behavior of $A$. In particular, we provide an explicit formula for the curvature form and derive normal forms for singularities of parallelizable equiangular webs. We also observe the emergence of polygonal structures near certain singularities.
Fields of Study & Subjects
Advanced Differential Geometry Research
Mathematics and Applications
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Differential Geometry and its Applications
- Volume
- 103
- Pages
- 102352–102352
- Publication date
- 17 February 2026
- Language
- EN