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arXiv · 2601.02325

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

Anton Petrunin·Sergio Zamora Barrera
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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.

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Anton Petrunin, Sergio Zamora Barrera. 2026-01-05. A translation of "What is differential geometry: curves and surfaces". https://arxiv.org/abs/2601.02325

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