A translation of "What is differential geometry: curves and surfaces"

TL;DR

This paper provides an accessible, problem-centered introduction to the fundamental techniques of differential geometry, focusing on smooth curves and surfaces for beginners and those considering the field.

Contribution

It offers an elementary, visual, and rigorous approach to core concepts in differential geometry, emphasizing essential techniques for newcomers.

Findings

Clear explanation of smooth curves and surfaces

Visual and elementary presentation of key techniques

Focus on problem-solving approach

Abstract

These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the techniques that are absolutely essential for further study, keeping it problem-centered, elementary, visual, and virtually rigorous.