Transversal intersection of Hypersurfaces in R^5

TL;DR

This paper develops algorithms to compute differential geometric properties and curvature measures of the transversal intersection curve of four hypersurfaces in five-dimensional Euclidean space, enhancing understanding of their geometric behavior.

Contribution

It introduces new algorithms for calculating geometric properties and curvature of intersection curves of four hypersurfaces in R^5, focusing on transversal intersections.

Findings

Algorithms for differential geometric properties are successfully derived.

The methods distinguish between transversal and nontransversal intersections.

Enhanced understanding of hypersurface intersection geometry in higher dimensions.

Abstract

In this paper we present the algorithms for calculating the differential geometric properties {t,n,b1,b2,b3,k1,k2,k3,k4} along-with geodesic curvature and geodesic torsion of the transversal intersection curve of four hypersurfaces (given by parametric representation) in Euclidean space R^5. In transversal intersection the normals of the surfaces at the intersection point are linearly independent, while as in nontransversal intersection the normals of the surfaces at the intersection point are linearly dependent.