Geometry of Fanning Curves in Divisible Grassmannians

TL;DR

This paper investigates the geometric properties of fanning curves in divisible Grassmannians, developing invariants that classify these curves and exploring their relation to classical invariants.

Contribution

It introduces a complete system of invariants for fanning curves in divisible Grassmannians and analyzes their geometric and classical invariant relations.

Findings

Constructed a complete set of invariants for fanning curves.

Analyzed the relation between new invariants and classical invariants.

Provided insights into the geometry of fanning curves in Grassmannians.

Abstract

We study the geometry of fanning curves in the Grassmann manifold of n-dimensional subspaces of $\mathbb{R}^{kn}$; we construct a complete system of invariants which solve the congruence problem. The geometry of the invariants themselves and their relation with classical invariants is also studied.