# Complete classification of surfaces with a canonical principal direction in the Minkowski 3-space

## TL;DR

This paper provides a comprehensive classification of all surfaces in Minkowski 3-space that have a canonical principal direction aligned with a fixed space-like or light-like direction, enriching the understanding of their geometric properties.

## Contribution

It offers a complete classification of surfaces with canonical principal directions in Minkowski 3-space, considering both space-like and light-like directions, which was not previously fully achieved.

## Key findings

- Complete classification of such surfaces achieved
- Characterization of surfaces with respect to space-like directions
- Characterization of surfaces with respect to light-like directions

## Abstract

In this paper, we characterize and classify all surfaces endowed with canonical principal direction relative to a space-like and light-like, constant direction in Minkowski 3-spaces.