# Order of contact and ruled submanifolds

## TL;DR

This paper generalizes classical theorems on osculation and ruled submanifolds using elementary geometric measure theory, expanding understanding of contact order in differential geometry.

## Contribution

It introduces a new generalization of the Monge-Cayley-Salmon theorem applying geometric measure theory to ruled submanifolds.

## Key findings

- Generalization of Monge-Cayley-Salmon theorem
- Application of geometric measure theory to contact order
- Enhanced understanding of ruled submanifolds

## Abstract

We prove a generalization of the Monge-Cayley-Salmon theorem on osculation and ruled submanifolds using elementary geometric measure theory.