Curvature lines of a transversal eq\"uiaffine vector field along a surface in $3$-space

TL;DR

This paper investigates how curvature lines behave near isolated umbilical points on a surface in 3D space when influenced by a transversal equiaffine vector field, providing insights into geometric properties in affine differential geometry.

Contribution

It analyzes the behavior of curvature lines at umbilical points under a transversal equiaffine vector field, a novel focus in affine differential geometry.

Findings

Characterization of curvature line behavior at umbilical points

Identification of geometric conditions affecting curvature lines

Insights into affine geometric structures near special points

Abstract

In this paper we discuss the behavior of the curvature lines of a transversal eq\"uiaffine vector field along a surface in $3$-space at isolated umbilical points.